{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "569d620b-882a-4d90-a82a-e0c2bb85de9d",
   "metadata": {},
   "source": [
    "\n",
    "姚端正、周国全、贾俊基《数学物理方法》第四版P.275\n",
    "\n",
    "伽辽金法重解例题3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e9220533-845d-4da3-88cf-4e204859b2e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *  # 导入sympy 包中所有的函数\n",
    "x, c0, c1, lamd = symbols('x c0 c1 lambda') # 自定义符号变量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "81a5c4fa-ff42-41c2-ba96-ca44ec677482",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = x*(x-1)*(c0+c1*x)  # 定义试探解，带入泛函并积分\n",
    "Phi = integrate(diff(y,x)**2,(x, 0, 1)) - lamd* integrate(y**2,(x, 0, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "80cd5009-4a79-49dc-9f95-8e97a7e92d55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{0}^{2}}{3} + \\frac{c_{0} c_{1}}{3} + \\frac{2 c_{1}^{2}}{15} - \\lambda \\left(\\frac{c_{0}^{2}}{30} + \\frac{c_{0} c_{1}}{30} + \\frac{c_{1}^{2}}{105}\\right)$"
      ],
      "text/plain": [
       "c0**2/3 + c0*c1/3 + 2*c1**2/15 - lambda*(c0**2/30 + c0*c1/30 + c1**2/105)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Phi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "25edbd4e-f5cc-4198-9adc-727b92971e53",
   "metadata": {},
   "outputs": [],
   "source": [
    "eq0 = diff(Phi,c0) # 泛函对参数c0求导\n",
    "eq1 = diff(Phi,c1) # 泛函对参数c1求导\n",
    "matrix_c = zeros(2) # 定义2*2零矩阵,用来存储系数的行列式矩阵\n",
    "c = [c0, c1] # 存储系数\n",
    "eqs = [eq0, eq1] # 存储方程\n",
    "for i in [0, 1]: # 计算行系数的列式矩阵\n",
    "    for j in [0, 1]: # 展开方程并获取c_j 项的系数\n",
    "        matrix_c[i, j] = expand(eqs[i]).coeff(c[j]) # 存储c_j 项的系数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "8cde541b-f8e3-4b99-9c4e-dfa60244ed66",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{2 c_{0}}{3} + \\frac{c_{1}}{3} - \\lambda \\left(\\frac{c_{0}}{15} + \\frac{c_{1}}{30}\\right)$"
      ],
      "text/plain": [
       "2*c0/3 + c1/3 - lambda*(c0/15 + c1/30)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "69f46e53-7489-42ea-988c-46b5bed6d127",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{0}}{3} + \\frac{4 c_{1}}{15} - \\lambda \\left(\\frac{c_{0}}{30} + \\frac{2 c_{1}}{105}\\right)$"
      ],
      "text/plain": [
       "c0/3 + 4*c1/15 - lambda*(c0/30 + 2*c1/105)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "19071805-db55-4ac0-b6d1-99449c30a5e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{2}{3} - \\frac{\\lambda}{15} & \\frac{1}{3} - \\frac{\\lambda}{30}\\\\\\frac{1}{3} - \\frac{\\lambda}{30} & \\frac{4}{15} - \\frac{2 \\lambda}{105}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[2/3 - lambda/15,     1/3 - lambda/30],\n",
       "[1/3 - lambda/30, 4/15 - 2*lambda/105]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_c\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4b7aea0c-06b2-4aec-a70b-83b5fa415006",
   "metadata": {},
   "outputs": [],
   "source": [
    "sol_lamd = solve(matrix_c.det(), lamd) # 求解本征值，存储到sol_lamd中．\n",
    "condition = integrate(y*y, (x, 0, 1)) - 1 # 归一化条件方程．\n",
    "# 把第一个本征值带入eq0, eq1和归一化条件方程中求 c0,c1的值，存储到sol_1．\n",
    "sol_1 = solve([eq0.subs(lamd, sol_lamd[0]),eq1.subs(lamd, sol_lamd[0]), condition], c0,c1)\n",
    "# 把第二个本征值带入eq0, eq1和归一化条件方程中求 c0, c1的值，存储到sol_２中．\n",
    "sol_2 = solve([eq0.subs(lamd, sol_lamd[1]),eq1.subs(lamd, sol_lamd[1]), condition], c0,c1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1bf60508-e940-4180-86eb-dcfe781257aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[10, 42]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol_lamd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2805e586-4b89-4da4-8641-9284c575db05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-sqrt(30), 0), (sqrt(30), 0)]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol_１"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "920c44c9-da68-42c3-90df-c6788b8986c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{0}^{2}}{30} + \\frac{c_{0} c_{1}}{30} + \\frac{c_{1}^{2}}{105} - 1$"
      ],
      "text/plain": [
       "c0**2/30 + c0*c1/30 + c1**2/105 - 1"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f5f452d0-820a-46ce-927b-22cb3c1e44eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-sqrt(210), 2*sqrt(210)), (sqrt(210), -2*sqrt(210))]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol_２ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6ef2fbce-3548-4085-897c-716e5217dd7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1VweaBHrQNNCTxgHu1K/hRl0fN5wdStYk9U7kmMycupDJyfOZRTOEB+KNGHOunRlsHOBB94a+dAv1Jbx2tTu7Bs94Dla9rK6EAeDTEAZMg1rtb/81xS2RQk7cCSnkbpMUckKUAVO2eqpv50z191614P6voE6X23o5Y3Y+G46fZ+3hZDYeu0BmXoHVeEM/d9rV8Sa8djXCa1ejZjXnMlkw/E4pikJcag6RZ1PZFXOJ3bGpnDyfaXWMm6MdXUN96NssgLsa1cDV8TaueFEUtQfdH69C1gVAp97d2nMyOMn7XFmRQk7cCSnkbpMUckKUsrjdsOIZuFjYIDP8Cej9P3B0L9HL5JjMrD2cxK/RCWw6fsHqdKmvuyPdQ33p3MCHiHrVqeFuux+aKZl5bDmRwsbjF9h0/AIXs0xFY452erqF+tK3uT+9m/iXvKjLTlXXbo0q7HjvHgj9PoVG95bin0BcJoWcuBNSyN0mKeSEKCUFeepSUlu/AMUC7gEwYDo06HXLL2G2KGw9mcKKqHj+PJRElslcNBbq50avxn7c3cSPsJpe6PUVb8btTlksCgfijfx5KInVBxKJveJGClcHA/3DAhnUNphWwV4lm3E8vRF+f1G9GQLU9Vv7vA/2zqX8J6japJATd0IKudskhZwQpSBxPyx/Bs4fUn/fYjD0/fCWF7Q/n57LT3vi+HFXHPFpOUX7a3m7MLBlIANaBlG/RtXqj6YoCkeTMvjjYBK/70sgJiWraKxBDTcGtw3mwdY1b/1Gifwc+Oc92DZN/b1fM3j4O/ANLYP0VZMUcuJOSCF3m6SQE+IOKAps/VJdncFSAC4+cN/n0GTALTxVIfLMJeZujWHtoeSiU6eezvYMCAtkYKsgWtcq4cxTJaUoCrtiUlmyJ47VBxLJzVcbFdsbdPRp6s/TXevRvKbnrb3YyfWw/Gn12jl7F/VUa8thZZi+6pBCTtwJKeRukxRyQtymvEz1jtTDv6q/b3Qf3PcFuPne9GkFZgt/HEzi2y0x7ItLK9rfpnY1hrWvxb3NA3CyL7+7S21Nem4+v0Un8NOeOPafMxbt71S/Ok93rUeXBj7/XvxmJMGypyBmo/r7FkOg3yclvo5RWJNCTtwJKeRukxRyQtyGi6dg8aNw4Yjar6zvh+p1VzcpIPLNFn7ec44Z/5wsOn3qYKfnwVZBPNEphEb+8v+vpA4lGPl2cwy/7UvAXDij2STAg6e71aVf8wDsbtbGxGJW12395331mkbvevDIPAhoUT7hKyEp5MSdkELuNkkhJ0QJnVgHv4yGXCO4+cGgH27ao6zAbGF5VDz/9/cJ4lLVAq66qwOPR9TmsQ618SnrZayqgHOXspmzJYbFu+LIyVdvEKlZzZkxXeoyqE3wzfvnndmufj/T48HgoM6qtnq0fIJXMpWxkLuTSxuqWDlxx6SQu01SyAlxixQFNn8Cf78HKFCzHQz6HjwCrnu42aLw+74Evlx/ouhCfR83R57tXo9h7WvJ6dMycCnLxA87zjBvWyyphW1M/D2cmNA7lIda18Rwozt9s1NhxbNw/A/1951eVHvO6eV7VBKVsZCbPn06zz33nNYxqgQp5G6TFHJC3IK8DFgxFo78rv6+zSi450Owu/aOSYtF4Y+DSXzx13FOFDa79XZ14JludXm8Q0i5rq5QVeWYzCyNjGPWxtNFp7Eb+bszsW8juoX6Xn+WxWKBDVNh00fq7xveCw9+I9fNlUBlK+ROnDhBbGwsd999t9ZRqoTS+vdTSis5CyEqjZSTMLunWsQZHKD//6l3pl6niNt6MoV+07YwbtFeTpzPxNPZnv/0acim//bgqa71pIgrJ84OBh6PCGH9y914/d7GeDjZcTQpgye+283jc3ZxKMF47ZP0erjrdXjwWzA4wrHVMPee4uXVRJXzzz//0L1791J/3e7duzN+/Pjbfv7FixepUaMGsbGxpZZpyJAhfPrpp6X2elqSGTkhRLHjf8IvYyDPqDb4HbwAara55rAkYy7/W3WYlfsTAXB3tGNU5zqM7lIHDyf78k4trpKWbWL63yf5fvsZTGYLOh080CqIV3o3JNDrOk2Bz+2BH4dC1nlw9YUhiyC4XfkHtzGVbUbu6tOqU6dOZdmyZRw9ehRnZ2c6duzIhx9+SMOGDUv0uqmpqdjb2+PufnuzvRMmTCAjI4PZs2ff1vOv5+DBg3Tt2pWYmBg8PW+xlU8pkxk5IUTp2j0HfhyiFnG1IuCpjdcUcflmC99sOkXPTzewcn8ieh080TGEza/24KW7Q6WIqyC8XBx4474mrH+5G/3DAlEUWLY3nh6fbODDNUfJumrtWmq2gTF/g19ztd/cvH6wb4k24YUmzp07R61ataz2bdy4kXHjxrFjxw7WrVtHfn4+vXv3Jisr6wavcn3e3t63XcRlZ2czZ84cRo8efVvPv5FmzZpRr149FixYUKqvqwUp5ISo6hQF/pkKqyaobSlaD4fhv4G7n9Vh206lcO+Xm3l/9VGyTGZa1/Li9+c78/aApni53OJqA6JcBXu7MG1oK34d14l2dbzJK7Awc8Mp+nyxiY3HL1gf7BUMo9ZAw35gNsHyp+Cvd9Rr6USlc/ToUY4fP170+7Vr115zbdyaNWt44oknaNq0KWFhYcybN4+zZ88SGRl5zestXbqU5s2b4+zsTPXq1enVq1dRwXf1qdXu3bvzwgsv8N///hdvb2/8/f15++23r5tz9erVODo60qFDh6J9jRs3RqfTXfcxffp0fvzxR5ydnUlMTCx6zsiRI2nRogVGY/FlBv3792fx4sUl+nuriKSQE6Iqs5hh5XjY+IH6+24T1WvirrgeLjk9lxd+jGLY7J2cOJ9JdVcHPn64BUuf6UjTQG1OSYiSCQv2YslTHfjm8XCCvJw5dymHEXN3MWFJNJcK73YFwNFNPZ3e+SX191s+U1eFMOdrE9zWKAqYsrR5lOAqKZPJxIoVK/j222+L9mVnZ+PsfPO1eC8XQd7e3lb7ExMTGTp0KKNGjeLIkSNs2LCBBx988KbtSObPn4+rqys7d+7ko48+YsqUKaxbt+6a4zZv3kx4eLjVvl9++QWA9evXk5iYSGxsLHq9np9//pkxY8YwZMgQQkNDef/99wGYPHkyf/31F3/88YfVadR27dqxa9cu8vLybvrnrujstA4ghNBIfg788iQcXQno1KWb2hafvjBbFL7bGsPn646TZTKj18FjHWrz8t0N8XSRU6i2RqfT0bupP53q+/Dxn8eYvz2WZVHxbDx+gckDmtK/RYB6d6teD73eBp9Q+PU5OPAT5KWrzYPtb/5BX+XlZ8P7gdp87dcSwMH1lg51cHDg1VdfpVu3bgBcuHCBGjVq3PQ5FouF8ePH06lTJ5o1a2Y1lpiYSEFBAQ8++CC1a9cGoHnz5jd9vRYtWjB58mQAGjRowPTp01m/fv01s4JnzpwhMND67zQ5ORk7Ozs6deqEo6MjkZGRWCwWunTpgqOj2qfyvffe4+GHH8bf359p06axefNmgoKCrF4nMDAQk8lEUlJSUW5bJDNyQlRFOZfghwfVIs7gqPaHu6KIO3cpm6Hf7OB/q46QZTLTMtiL357rzJT7m0kRZ+NcHe14e0BTfhnbkVA/Ny5mmXjhxyienL+HhMLWJYC6HuuQRWDnBMfXwIKHITddu+CiVOl0Olq0aEF0dDRr1qzhnnvuuenx48aN4+DBg9c9FRkWFkbPnj1p3rw5jzzyCLNnz+bSpUs3fb0WLaxXFAkICOD8+fPXHJeTk3PNjQAHDhwgNDS0qGjbt28fNWrUwM+v+HKQ++67jyZNmjBlyhSWL19O06ZNr3ntyzOQ2dnZN81a0cmMnBBVjTEeFj4M5w+DowcM/RFCOhcN/7YvgdeXHyAjtwBXBwNv3NeEwW2C0d+ouaywSa1rVWPl812YueEU0/85wfqj59n5+SZevachj7avrX6/G94Djy1Tb4I5swXm36f+3tVH6/gVk72LOjOm1dcuoYceeohffvkFPz+/m3ZxeO6551i5ciWbNm2iZs2a14wbDAbWrVvHtm3bWLt2LdOmTeP1119n586d1KlT5/px7a1/INTpdFiucz2mj4/PNUXh/v37rWb89u3bd80M4Jo1azh69Chms9mqwLtSamoqAL6+N18vuqKTGTkhqpKUEzCnt1rEufnDyD+KiriM3HwmLInmhR+jyMgtoFUtL/54sStD29WSIq6ScrDT82KvBqx+oQvhtauRmVfAm78eYvA32zl3qXCWIqQTjPgdXHwgcZ/aa854TtvgFZVOp57e1OJxG0trde3albVr196w/YaiKDz33HMsX76cv//++4ZFmfpH19GpUyfeeecdoqKicHBwYPny5SXOdLVWrVpx+PBhq3379++3mtHbt2+f1e/37t3LoEGDmDNnDj179uTNN9+87msfPHiQmjVr4uNj2z+YSCEnRFWRcgLm3Qfp56B6fRi9FvzVa10iz1zi3v/bzLKoePQ6eLFnA35+OoJa1Uv+U76wPQ383Pn56Qim3N8UVwcDu2Mvce+Xm1lzMEk9ILClekerR024eALm9FEbRwubZjAYaNWq1Q1Pq44bN44FCxawaNEi3N3dSUpKIikpiZycHKvjdu7cyfvvv8+ePXs4e/Ysy5Yt48KFCzRu3PiOM/bp04dDhw4VzcpZLBYOHTpkVbidOnWKkJAQAGJjY+nXrx+vvfYaQ4cOZcqUKfzyyy/s3bv3mtfevHkzvXv3vuOMWpNCToiqIOWkWsRlJkGNJjDqT6hWmwKzhS/+Os6gr7cTl5pDzWrO/PR0BC/dHYqdQd4eqhK9XsfwiBDWjO9KWLAX6bkFPLMgkrd+PUhuvhl8GqjFXPUG6g8Dc/tA0kGtY4s7NG3atBueWpw5cyZGo5Hu3bsTEBBQ9FiyxLrHoIeHB5s2beLee+8lNDSUN954g08//ZS+ffvecb7mzZvTunVrfvrpJ0At2rKzs60KuebNmzN58mS2bt3KPffcw/3338/EiRMBaN++PX379uW1116zet3c3FxWrFjBmDFj7jij1mRlByEqu4un1AavGYlqETfid3D1IS41mxcXR7H3bBqgdv5/5/6m0tRXYCqw8OnaY3y96TQAjQM8mD6sFfV83SArBRY8qJ5mdfGBJ1ZBjUYaJ9ZGZVvZoaJatWoV//nPfzh48CB6fen8gDlz5kyWL1/O2rVrS+X1boes7CCE+HdXFnG+jWH4bygu1VkedY6+X25m79k03B3t+HJISz4f3FKKOAGo185Nurcx80a2pbqrA0cS0+k/bQtLI8+pNzoM/w0CwiA7Beb3V0/bC1FG+vXrx1NPPUV8fHypvaa9vT3Tpk0rtdfTkszICVFZXTylnk7NSADfRjBiJUaDF2+uOMhv+9Q769rUrsbng1sS7C3XwonrS07P5aUl0Ww7dRGAB1sFMWVgM9zM6TB/ACQfUNflfWIVVK+ncdryJTNy4k7IjJwQ4sauKeJ+53C6I/3+bzO/7UvAoNcx4e5QFj/VQYo4cVN+Hk78MLo9r/QORa+DZVHx9J+2hUNpBhi+Qp3pzUhUi7pLZ7SOK0SVI4WcEJVN6mn1dFdGAvg0hBG/sybWwkMzt3HuUg61vF34+ZkIXujZQG5oELfEoNfx3F0NWPJ0BAGeTsSkZPHwzO2sOpUPI35TV4FIP6f2mZPWJEKUK3kXF6IySY2Bef0hPR58QlFG/Ma0nUaeWRBJTr6ZLg18+P25zrSuVU3rpMIGtQ3xZvULXega6ktOvplxi/by2fY0LI//Ct51Ie1sYYsbjZriClEFSSEnRGVxKba4T5xPKLmP/soLKxP5dN1xAJ7oGMJ3T7SVJbbEHanm6sDcEW14srPaHPb/1p/g2d8SyR66Arxqw6UY9TRrRrK2QctRFbvUXJSS0vp3I4WcEJVBVoq6dmr6OajegPMPLGXQwtP8vi8BO72O9x9oztsDmsqpVFEq7Ax63rivCR893AIHg541h5J4cOEZEgb+XNw0+PsB6r/LSuzyMlO2vlan0MblfzdXL1dWUnLXqhC2Li9TvSYuYS94BnOo71JG/nKO8xl5VHOxZ+Zj4XSoW13rlKKSijyTytM/7CUlMw9vVwe+G+BD2F9D1Rsg/FvAyNXg6K51zDKTmJhIWloaNWrUwMXFBd1tLJUlqhZFUcjOzub8+fN4eXkREBBwR68nhZwQtsycDz8OhZPrwNmb9R2/59k/M8krsBDq58a3w9vKMluizCWk5TDm+z0cSkjH3qDj855u3Bc5CrIuQL2eMGwJGCrnKX1FUUhKSiItLU3rKMLGeHl54e/vf8fFvxRyQtgqRYEVY2Hfjyh2zixsNI039qhFW89GNfhiSEvcpcGvKCc5JjOvLN3Hqv2JALzTJo/hx8ahy8+Glo/C/TNua2F3W2E2m8nPz9c6hrAR9vb2GAyGUnktKeSEsFV/vQ1bPkfRGfjKfwofx6gXnz/TrR7/6dMQg77yfmiKiklRFP5v/Uk+/0u9weathnGMPPsaOsUMXf8Ld72ucUIhKh+58lkIW7RjFmz5HIDZXi/ycUwdHAx6PhsUxsS+jaSIE5rQ6XS82KsBHzzYHL0OphwL5nvvF9XBTR9B5DxN8wlRGUkhJ4StOfgLrJkIwAKX4byf2AZXBwPzRrXlwdY1NQ4nBAxpV4uZj4XjYKdncnwblroOVQdWToDjf2obTohKRgo5IWzJ6Y2w/BlA4TeHfryR2gcvF3sWjulAx3o+WqcTokifpv78MKod7k52vHLxPtba9wTFDD8/AfGRWscTotKQQk4IW5G4HxY/CmYTGwwRjE8fSg13J356OoKWwV5apxPiGu3rVuenpyPwdXfi2YwR7NS3hPxsWDhIXUpOCHHHpJATwhYYz8HCh8GUQaSuKU9nPU1NbzeWPtORUL/K26NL2L7GAR4sG9uRmtU9GJX9PEeoA9kpsOChSt8wWIjyIIWcEBWdKVvtFZeZzAmCGZkznhC/6ix9JkJ6xAmbEOztwtKxHakb5M/w3FeIV3zVGbkfh6j/voUQt03TQm7Tpk3079+fwMBAdDodK1asuOnxy5Yt4+6778bX1xcPDw8iIiL480+5cFZUYooCvz4LSftJVdwZmfcKdYODWPJ0B2p4OGmdTohb5uPmyI9PdSC0fn2Gm/5LmuIK53bDL0+Cxax1PCFslqaFXFZWFmFhYcyYMeOWjt+0aRN33303q1evJjIykh49etC/f3+ioqLKOKkQGtn0CRxaTr5i4BnTeGrXa8TCJ9vj5eKgdTIhSszN0Y65T7QltGk4T5peJk+xh2Or4J/3tI4mhM2qMA2BdTody5cvZ+DAgSV6XtOmTRk8eDBvvfXWLR0vDYGFzTjyOyx5DICJ+U+S2nAo/ze0FU72pdMNXAit5JstjF8cjd2hn/nS4St158NzodlD2gYTwgbZ9DVyFouFjIwMvL29b3hMXl4e6enpVg8hKrzkQxQsHQPAvILemMIe56tHW0sRJyoFe4OeL4a0pKDpI3xd0A8A8/Jn1TuzhRAlYtOF3CeffEJmZiaDBg264TFTp07F09Oz6BEcHFyOCYW4DVkpZM9/BDtzDlvMTTkd/hqfPByGncGm/7sKYeVyMXeg0UtsMjfHYM4l54fBcierECVks58MixYt4p133uGnn36iRo0aNzxu0qRJGI3GokdcXFw5phSihApMpH43BJfseGItfvzd7EPevr8lellyS1RC9gY9nw8N57cG7xFj8cM5O4FL84aAWRafF+JW2WQht3jxYp588kl++uknevXqddNjHR0d8fDwsHoIUVHFL34B75TdZCjOLK7/Ea8/0lmKOFGp2Rv0TH20CwtCPiBDcabahd3E/fii1rGEsBk2V8j9+OOPjBw5kh9//JF+/fppHUeIUnNq1RcEnfwRi6JjQeCbvPLoAAxSxIkqwN6gZ+KIgSwMfB2A4JMLObLy/zROJYRt0LSQy8zMJDo6mujoaABiYmKIjo7m7NmzgHpadPjw4UXHL1q0iOHDh/Ppp5/Svn17kpKSSEpKwmg0ahFfiFJzZOvv1N71DgDLvEfz5JNj5Zo4UaXYG/SMfnIcv1cfBUC93W+zb+sajVMJUfFp2n5kw4YN9OjR45r9I0aMYN68eTzxxBPExsayYcMGALp3787GjRtvePytkPYjoqI5eHAfNX++Fy9dJttcehL+0k842ttpHUsITeQXmNn/+UDCszaRoniSNPgPmjVpqnUsISqsCtNHrrxIIScqkkNnktF914cmxHDSPpSaL/2Dk4ub1rGE0FRetpHkz7tTK/80h6iLw5i1NAjy1TqWEBWSnLsRQiPHkzM4/N04mhBDus6DoKeXShEnBODo4onPk0tJ13nQlNPsn/MscamyJqsQ1yOFnBAaSEjLYeE3H/MI67Cgw27QHJx9amsdS4gKw8WvHvqHvsGCjocsa5n39UdcyMjTOpYQFY4UckKUM2N2Pm9++wv/LZgFgCliAi6Ne2ucSoiKx61ZX7LbjwdgQu5XvD77F9JzpcecEFeSQk6IcpSbb+a5+Vt4Nf19XHV55NbsjNPdr2sdS4gKy63Pm+QEdcJVl8fLae/x7HdbyDGZtY4lRIUhhZwQ5cRiUZiwJIqBCZ8Qqo8n36UGTkO+A72snyrEDekNOA/5jnxnXxrqz3F//GeMW7SXfLNF62RCVAhSyAlRDhRFYcrKw7gfWcxDhi0oOj32g+aB242XlxNCFHL3w37QXBSdnkfsNlH9xE+89etBqljTBSGuSwo5IcrBN5tOs2v7BqbYzQNAd9ebENJJ21BC2JI6XdH1eA2Ad+2+I2r3VmZtPK1xKCG0J4WcEGVsRVQ80//Yywz7L3HU5UODPtBpvNaxhLA9nV+Gej1x0uUzw/5Lpq+JYtX+RK1TCaEpKeSEKENbTqTwn6XRfGD/DXX0yeAZDA/MAr381xOixPR6eHA2uAdST5/IVPtveemnKCLPXNI6mRCakU8TIcrIoQQjzyyIZBh/0s+wC0VvD4/MBxdvraMJYbtcq8Mj81D0dgwwbOcRZR1jvt/DmYtZWicTQhNSyAlRBs5n5PLk/D3UNJ3mDftFAOh6/w9qhmucTIhKoFZ7dL3eBuAt+wVUzz7NyHm7Scs2aZtLCA1IISdEKcvNN/PU95GkGtOZ6fwV9uRDaF9o/7TW0YSoPDqMg3o9ccTEV04zOHchjad/iCSvQHrMiapFCjkhSpGiKExadoDouDQmOy2hjuUsuNaA+6eDTqd1PCEqD70eBs4El+o0UM7wuuNP7IxJZdIvB6QtiahSpJATohTN2nia5VHx9DREM4w/1J0DZ4Krj7bBhKiM3P3g/q8AGKFbRTfDAZZFxfPl+hMaBxOi/EghJ0QpWXc4mY/+PEp1jEx3/Vbd2X4sNOilbTAhKrOG90DbJwGY5TYbb9L54q8TrDkobUlE1SCFnBCl4EhiOi8ujkJRFBbW+AFnUyrUaAKFF2QLIcpQ7/+BT0Oc81L40W8BoDDhp30cTUrXOpkQZU4KOSHu0MXMPJ6cv4dsk5m3/LbTKH0bGBzhoW/B3knreEJUfvbO8PAcMDjQ0LiFt/x3kG1SbzqSO1lFZSeFnBB3wFRg4ZkFkcSn5dC12kVGZhWeUr17Cvg11TacEFWJf/OiGfCRmd/S2SuFs6nZPLcoigKzRdtsQpQhKeSEuE2KovDGigPsjr2Et6PCbJeZ6ApyoX4vaTUihBbaj4V6d6EryOFb11l4OljYcjKFD/44qnUyIcqMFHJC3KYFO87w055z6HXwa6P1OF48DC7V1bvopNWIEOXvipYkThcPs6LhXwB8uyWGZXvPaRxOiLIhhZwQtyE6Lo0pKw8DMK19GsHH5qoD989QWyIIIbTh7g8DpgNQ58Q8PgxXb3iYuOwA++LSNAwmRNmQQk6IEkrNMvHsgkjyzQoPNnLl3lPvqgNtRkPDvtqGE0JAo3uh9XAABsVPpV9Dd0wFFp7+IZLzGbkahxOidEkhJ0QJmC0KLy6OIsGYSx0fVz50XYguIxGq11dbIAghKobe74FnMLq0M3zuvYx6vq4kpefy3EK5+UFULlLICVEC/7f+BJtPpOBkr+eHThewP/QT6PQwcBY4uGgdTwhxmZOHujQe4BD1HQt6ZOPmaMeu2FQ+XntM43BClB4p5IS4RRuOnef//laX/vn0vmBqbnlNHej4PAS31TCZEOK66nYvWvUhYON/+ez+ugB8vfE06w4naxhMiNIjhZwQt+DcpWzGL4lGUeDR9rXoF/c5ZJ0H30bQ/TWt4wkhbqTXO+BVG4xx9D73f4zsFALAyz9FE5earW02IUqBFHJC/Iu8AjPPLtxLWnY+LWp68nb9k3BwKegMMPArWb1BiIrM0U39fwqw93teC42nVS0v0nMLGLswktx8s7b5hLhDUsgJ8S/eXXmY/eeMeLnYM+uBWtj/8Yo60PklCArXNpwQ4t+FdFabBQP2K19kxoP1qOZiz8H4dN4tbCMkhK2SQk6Im1i29xwLdpxFp4MvBoURuPUNyE6BGk2h23+1jieEuFU93wLvepCRQOCOKXw+uCU6HSzceZYVUfFapxPitkkhJ8QNHE1K57XlBwB44a4GdC/YAod/Bb0dPDAT7Bw1TiiEuGUOLuqqD+ggeiHd2ctzPeoDMGnZAU4kZ2ibT4jbJIWcENeRkZvP2AV7yc230DXUlxfae8Cql9XBrv+BgDBtAwohSq5We+j4nLr9+wuM7+RLx3rVyck3M3bhXrLyCrTNJ8RtkEJOiOt4c8VBYlKyCPR04otBYRhWvww5l8C/OXR5Wet4Qojb1eN18AmFzGQMa17lyyGtqOHuyMnzmbz560Gt0wlRYlLICXGV5VHnWBGdgEGvY9qw1nifWQ1HV4LeXm38a7DXOqIQ4nbZO6v/j3V6OPATvufWMn1Ya/Q6WLY3nl+j5Xo5YVukkBPiCmcvZvPmikMAvNizAeG+Cqz+jzrYZQL4N9MwnRCiVNQMh07j1e1VL9POX8/zdzUA4I3lB6W/nLApUsgJUSjfbOGFxVFk5hXQLsSbcT3qw9o3IesC+DSUU6pCVCbdXoXqDSAzGf6azPN31Se8djUy8gp4cbGsxypshxRyQhT6v/UniI5Lw93Jjs+HtMQQswGiFwA6GDBN7lIVojKxd4L+X6rbkfOwi9vOF4Nb4u5ox96zafzf3ye1zSfELZJCTghg5+mLTP9HfeOe+mBzglws8PuL6mC7MerdbkKIyiWkE7QeoW7//iLB7nr+94B6+cT0v0+wKyZVw3BC3Bop5ESVZ8zO56XCdVQfCa/JfS0C4Z/3Ie0MeNRUG4kKISqnu6eAmx9cPAGbP+X+lkE82DoIiwIvLYnGmJOvdUIhbkoKOVGlKYrCa8sPkGDMJaS6C28PaArxkbCjcG3G+z4HR3dtQwohyo6zF/T9UN3e8jmcP8KU+5tRy9uF+LQcXlt+AEVRNI0oxM1IISeqtJ8jz7HqQCJ2eh1fDmmFq50Cvz4PigWaPwKhvbWOKIQoa00GQmhfsOTDby/gZq/n/4a2wk6vY9X+RJZGntM6oRA3JIWcqLJOX8jk7d/UViMv925IWLAXbP0Czh8CZ2+45wNN8wkhyolOB/0+AQc3OLcL9syhZbAXL90dCsDk3w4Rk5KlcUghrk8KOVElmQosvLg4mmyTmYi61Xm6a11IOQEbP1IPuOcDcPXRNqQQovx41oSek9Xtv94BYzzPdKtHh7reZJvMvLg4ClOBtCQRFY8UcqJK+mzdcQ7EG/FyseezwWHodcDKl8Bsgno9ocUgrSMKIcpb29FQsy2YMmD1Kxh08Pnglng627P/nJHP1h3XOqEQ15BCTlQ5206m8PWmUwB88GALAjydYf9PELsZ7Jyg36fqqRYhRNWiN0D//1OX4zu2Gg7/SoCnMx8+1ByArzedkpYkosLRtJDbtGkT/fv3JzAwEJ1Ox4oVK/71ORs2bKB169Y4OjpSv3595s2bV+Y5ReWRnpvPyz/vQ1FgaLta3NPMH3IuwdrX1QO6/ge862gbUgihHb8m0Hm8uv3HfyHnEvc0C2BQm5ooCrzy8z6y8go0jSjElTQt5LKysggLC2PGjBm3dHxMTAz9+vWjR48eREdHM378eJ588kn+/PPPMk4qKov/rTxMYmGrkTfva6zuXD+lcBmuUOj4grYBhRDa6/JK8fJd69Tr5t68rwlBXs6cTc1m6h9HNA4oRDGdUkEa5Oh0OpYvX87AgQNveMyrr77KqlWrOHjwYNG+IUOGkJaWxpo1a677nLy8PPLy8op+n56eTnBwMEajEQ8Pj1LLLyq+f46eZ+S83eh08NPTEbQN8YZze+DbXoACI1ZCnS5axxRCVASxW2Hever26L8guC1bT6bw6Lc7AfhhdDu6NPDVMKAQKpu6Rm779u306tXLal+fPn3Yvn37DZ8zdepUPD09ix7BwcFlHVNUQMbsfCYu2w/A6E511CLOXAArxwMKhA2VIk4IUSykE7R8VN1eNQEsZjrV92F4RG0A/rt0P+m5suqD0J5NFXJJSUn4+flZ7fPz8yM9PZ2cnJzrPmfSpEkYjcaiR1xcXHlEFRXMO78fIjk9j7o+rrzSp6G6c9c3kHQAnLzg7nc1zSeEqIB6vQNOnpC0H3bPAWBi30bUru5CojGXd38/rHFAIWyskLsdjo6OeHh4WD1E1bL2UBLLouLR6+CTQWE42RsgPQH+eU89oNfb4CanSIQQV3HzLV5r+e//QeZ5XBzs+PSRMHQ6dWWY9UeStc0oqjybKuT8/f1JTrb+T5OcnIyHhwfOzs4apRIV2aUsE68tV6+pfKprPVrXqqYOrJkIpky1Z1TrERomFEJUaOEjIaAl5Blh7ZsAtAnxZkyXugBMXHaAS1kmDQOKqs6mCrmIiAjWr19vtW/dunVERERolEhUdJN/O0RKZh4NargxvlcDdeeJdXD4V9AZ4L7PQW9T/w2EEOVJb4B+nwE62L9YvQkCmHB3KPVruHEhI4+3Cpf6E0ILmn6CZWZmEh0dTXR0NKC2F4mOjubs2bOAen3b8OHDi45/5plnOH36NP/97385evQoX331FT/99BMvvfSSFvFFBffHgUR+25eAQa/jk0cKT6nm58DqV9QDOowF/+bahhRCVHw1wyG8cOZ+1ctgzsfJ3sCnj4Rh0Ov4fV8Cq/YnaptRVFmaFnJ79uyhVatWtGrVCoAJEybQqlUr3npLvSYhMTGxqKgDqFOnDqtWrWLdunWEhYXx6aef8u2339KnTx9N8ouKKyUzj9dXqKdUx3arR1iwlzqw+VO4FAvugdB9omb5hBA2pudkcPaGC0dg59cAhAV78Wz3egC8seIAFzLybvYKQpSJCtNHrrykp6fj6ekpfeQqMUVReHbhXv44mEQjf3d+fa4TjnYGSDkBX0WAJR8G/QBNBmgdVQhhS/Z+D789Dw5u8Nxu8AjEVGDh/hlbOZKYTr8WAcwY1lrrlKKKkYuDRKWzcn8ifxxMwq7wlKqjnQEURb3BwZIP9e+Gxv21jimEsDUtH4Oa7dQbpf5Ul/VzsNPz8cMtMOh1rNqfyLrDcherKF9SyIlKJTXLxOTCC4+fu6s+zYI81YHja+DkX+pi2H0/BJ1Ow5RCCJuk10O/T0Gnh0PL4PQGAJoFefJkF3WN5jdWHJBGwaJcSSEnKpX/rTxMapaJRv7uPNu9vrozP1edjQOIGAfV62kXUAhh2wJaQNsx6vaqV6BAvS7upV6hhFR3ITk9jw/+OKphQFHVSCEnKo1Nxy+wLCoenQ6mPtgcB7vCf947Zqg3OLj5Q9dXNM0ohKgE7nodXGvAxROwfToATvYGpj7YAoBFO8+y4/RFLROKKkQKOVEpZJsKeH3FAQBGRITQ6nLjX2M8bPpE3b57Cji6a5RQCFFpOHlC7/+p2xs/hjS1u0JEveoMbaeu5z1p2QFy881aJRRViBRyolL48q8TxKXmEOjpVLyWKsBfkyE/W71AucUg7QIKISqXFoOgdicoyCm68QFgYt/G1HB3JCYliy/Xn9AwoKgqpJATNu9gvJFvt8QA8O7AZrg52qkDZ7bDgZ8BHdz7kdzgIIQoPTod3PuxeuPDkd8gZjMAns72vDuwGQDfbDrNwXijlilFFSCFnLBpBWYLE5ftx2xR6NcigJ6N/dQBixn++I+63Xo4BLbSLqQQonLyawptRqnbayap7ztAn6b+3NvcH7NFYeKy/RSYLRqGFJWdFHLCpn23NZaD8el4ONkxuX+T4oG98yHpADh6Qs+3tAsohKjcur+mXjOXfEBtGFzo7QFN8XS252B8etEZAyHKghRywmbFpWbz2brjALzerzE13J3UgexUWP+uut3jNXD10SihEKLSc62uFnMAf78LOWkA1HB34o1+jQH4fN1xzlzM0iigqOykkBM2SVEUXlt+gJx8Mx3qejOoTXDx4IapkJMKvo2h7WjtQgohqoa2o8GnIWRfhE0fF+1+OLwmnev7kFdg4a1fD1HFVsQU5UQKOWGTVkTHs/lECg52eqY+2ALd5RsZkg/B7m/V7b4fgMFeu5BCiKrBYA/3vK9u75ylrusM6HQ6ptzfFAeDno3HL/DHwSQNQ4rKSgo5YXNSs0y8u/IIAC/2bEAdH1d1QFHgj1dBsUDjAVC3u3YhhRBVS/1e0KAPWAqs2pHU9XVjbHd1NZl3fj9EhizfJUqZFHLC5kxdfYTULBMN/dx5qmvd4oHDKyB2M9g5FTfrFEKI8tLnfdDbwYk/4cRfRbvHdq9XtHzX5+ukt5woXVLICZuyJzaVnyPPAfD+g82xNxT+EzZlw59vqNudxkO12toEFEJUXT71of0z6vafk8Cszr452RuYcr/aW27ethjpLSdKlRRywmYUmC28seIgAIPbBBNeu1rx4NYvIP0ceAZDpxe1CSiEEF3/Ay4+kHK8+HpdoGuoL/e1CMCiwOsrDmK2yI0PonRIISdsxvfbz3A0KQMvF3te7duoeMB4DrZ+qW73fhccXLQJKIQQzl5wV+HZgQ1TIeti0dCb9zXBzdGOfXFp/LjrrDb5RKUjhZywCefTc4t6xv23TyO8XR2KB9e/CwW5UKsjNBmoTUAhhLis9XDwaw65RvjnvaLdfh5OvNI7FICP1hzlQkaeVglFJSKFnLAJ760+QmZeAWHBXgxpe0XPuPi9sH+xut3nPVlPVQihPb1BbX8EEPmd2hap0OMRITQL8iA9t4D3Vx/RKKCoTKSQExXetlMp/BqdgE4H/7u/GXp9YbGmKLC28BRG80EQ1Fq7kEIIcaWQzmobJMUCayaq71eAQa/jvYHN0elgeVQ8206laBxU2Dop5ESFZirsiA7wWPvaNK/pWTx4dBWc2aq2G5H1VIUQFU3vd8HgCDGb1PerQmHBXjzWXr2z/o0VB8krMGuVUFQCUsiJCm3u1hhOns+kuqsDr/RuWDxQYIJ1hcVbxDjwCr7+CwghhFaqhUDH59Ttta9DQfE1ca/0aYiPmyOnL2Qxd0usJvFE5SCFnKiwEtJy+PIvtXnmpHsb4+lyxXJbe+ZC6ilw9YXOL2mUUAgh/kXnCeDmD5diYdfsot2ezva8dq969/20v0+QnJ6rUUBh66SQExXWuysPk5Nvpm1INR5qHVQ8kHMJNhZeSNzjNXB01yagEEL8G0c3uKtwya5NH0N2atHQwJZBtK7lRbbJzFS58UHcJinkRIV0eYFpg17HuwObobvybtRNn6jFnG8jaDVcu5BCCHErWj4KNZpAbhps/rRot16v4+0BTdHpYEV0AntiU2/8GkLcgBRyosIxFVh4+zf1BocnOobQyN+jeDD1NOz8Wt3u/R4Y7DRIKIQQJaA3wN3vqtu7voHUmKKhFjW9GNxGvcZ38m+HZMUHUWJSyIkKZ/62WGJSsvB1d2R8rwbWg3+9DZZ8qHcXNOilST4hhCix+j2hbg8wm2D9FKuh//RpiLuTHYcS0lmyO06jgMJWSSEnKpQLGXn833r1Bof/9mmIu9MVNzic2Q6HfwWdHnr/T6OEQghxG3Q6tR0JOji0DM7tKRqq7ubIhLvVFR8+/vMoxux8jUIKWySFnKhQPl17jIy8AlrU9OSh1jWLBywW9fZ9gFaPgV9TbQIKIcTt8m+uXi8HajNzpfg06mMdahPq58al7Hw+/+u4RgGFLZJCTlQYB+ONLNmjnlaY3L9J8QoOoP4EGx8J9q7Q4w2NEgohxB2663Wwc4az2+HoyqLd9gY9k/urP6D+sOMMR5PStUoobIwUcqJCUBSFd34/hKLA/S0DCa/tXTyYn6NeGwdqzzh3P00yCiHEHfMILG4SvG4ymItPo3aq70PfZv6YLQpv/3YIRZEbH8S/k0JOVAirDiSyO/YSzvYGJvZtZD24cxYY48A9UF3FQQghbFmnF9Vm5qmnYM93VkOv3dsYRzs9O06nsvpAkkYBhS2RQk5oLsdkZurqowA8060eAZ7OxYPZqbD5c3W755vg4KJBQiGEKEWO7tB9krq9YSrkGouGgr1dGNu9HgDvrTpMjknWYRU3J4Wc0Nw3m04Tn5ZDkJczT3Wtaz245TPIM0KNptBisDYBhRCitLUeAT6hkJMKmz+zGnqmWz2CvJxJMOYyc+MpjQIKWyGFnNBUQloOMzeeBGDSvY1wdjAUDxrPwc5v1O1ek9WmmkIIURkY7IqbBO+YCWnF/eOc7A280a8xALM2nuLcpWwtEgobIYWc0NSHa46Sm2+hXYg3/ZoHWA9umArmPKjVERr01iagEEKUldA+ENJFfZ/b8IHV0D3N/OlQ1xtTgYWP/zymUUBhC6SQE5rZE5vKr9EJ6HTwVv8m1uupnj8K0YvU7bvfUZtpCiFEZaLTQa+31e19i9T3vaIhHW/0a4JOB79GJxAdl6ZJRFHxSSEnNGGxKLzz+2EABrcJplmQp/UBf78LigUa3QfB7TRIKIQQ5aBmG2jcX32/u2rprmZBnjzYSm2M/t6qw9KORFyXFHJCE0v3nuNAvBF3Rzte7t3QejBul9ooU6eHnm9pE1AIIcrLXW+p73fHVsHZnVZD/+nTECd7PbtjL7HmoLQjEdeSQk6Uu2xTAZ+uVa/5eL5nfXzdHYsHFaW4+W/LYeDb8NoXEEKIysQ3VF16ENT3vytm3vw9nXiqi3o3/wdrjmIqsGgQUFRkUsiJcvft5hiS0/MI9nZmRMcQ68ET6+DMVjA4FvdZEkKIyq77JLBzgrPb4PifVkNPd6uHr7sjZy5m8/32WG3yiQpLCjlRri5k5PF1YV+k//RphKPdFS1FLObi2bj2T4FnzfIPKIQQWvAIhPZPq9vr31HfDwu5Otrx8t2hAEz7+yRp2SYtEooKSgo5Ua6++Os4WSYzYcFe9G9xVbuRAz/D+UPg6AmdJ2gTUAghtNL5JXDyhPOHYf9PVkOPtAmmkb87xpx8/m/9SY0CiopI80JuxowZhISE4OTkRPv27dm1a9dNj//iiy9o2LAhzs7OBAcH89JLL5Gbm1tOacWdOHk+k8W71aaXr9/b2LrdSEEe/P2eut35RXDx1iChEEJoyLmaWswB/PO++r5YyKDX8dq9apPgH3bEEpuSpUVCUQFpWsgtWbKECRMmMHnyZPbu3UtYWBh9+vTh/Pnz1z1+0aJFTJw4kcmTJ3PkyBHmzJnDkiVLeO2118o5ubgdH/xxFLNF4e4mfrSrc1WhtmcuGM+Cmz+0H6tNQCGE0Fq7p8E9QH0/3D3HaqhrqC/dQn3JNyt88MfRG7yAqGo0LeQ+++wzxowZw8iRI2nSpAmzZs3CxcWFuXPnXvf4bdu20alTJ4YNG0ZISAi9e/dm6NCh/zqLJ7S34/RF/jqSjEGvY2LfRtaDuemw6WN1u/ur4OBS/gGFEKIicHCB7hPV7c2fqO+PV3i9X2P0OlhzKIldMakaBBQVjWaFnMlkIjIykl69ehWH0evp1asX27dvv+5zOnbsSGRkZFHhdvr0aVavXs299957w6+Tl5dHenq61UOUL4tF4f3VRwAY1q4W9XzdrA/YPh2yL0L1+tDqcQ0SCiFEBdLyMajeQH1f3DbNaijUz50h7WoBapNgi0WaBFd1mhVyKSkpmM1m/Pz8rPb7+fmRlHT9pofDhg1jypQpdO7cGXt7e+rVq0f37t1vemp16tSpeHp6Fj2Cg4NL9c8h/t3v+xPYf86Im6MdL/ZqYD2YeR62TVe373oTDPblH1AIISoSg11xM/TtM9T3ySu81CsUVwcD+84Z+X1/ggYBRUWi+c0OJbFhwwbef/99vvrqK/bu3cuyZctYtWoV77777g2fM2nSJIxGY9EjLi6uHBOL3HwzH61Rm/8+060uPm6O1gds+hjysyCwNTS5X4OEQghRATXuD0Ft1PfHjR9ZDfm6O/Jsj/oAfLTmGHkF5uu9gqgiNCvkfHx8MBgMJCcnW+1PTk7G39//us958803efzxx3nyySdp3rw5DzzwAO+//z5Tp07FYrl+t2tHR0c8PDysHqL8fL89lvi0HPw9nBjdua71YGoM7PlO3e71trqAtBBCCPX9sNfb6nbkd3Ap1mp4dOc6+Hk4Ep+Ww8IdZ8s9nqg4NCvkHBwcCA8PZ/369UX7LBYL69evJyIi4rrPyc7ORq+3jmwwqA1lZTHhiict28T0v9V+Ry/3DsXZwWB9wD/vgSUf6t0FdbtpkFAIISqwOl3U90dLAWz40GrIyd7A+F5qk+Dp/5wkIzdfi4SiAtD01OqECROYPXs28+fP58iRI4wdO5asrCxGjhwJwPDhw5k0qXiZpv79+zNz5kwWL15MTEwM69at480336R///5FBZ2oOKb9fZL03AIa+bvzYOurVmlI3K82AIbinzqFEEJY6/GG+uv+xXDhmNXQI+E1qevjSmqWiW83x2gQTlQEdlp+8cGDB3PhwgXeeustkpKSaNmyJWvWrCm6AeLs2bNWM3BvvPEGOp2ON954g/j4eHx9fenfvz/vvfeeVn8EcQPnLmXzw/YzALx2b2MM+qtOm/79P/XXZg9BQFg5pxNCCBtRMxwa9oNjq9QmwYPmFw3ZGfS80qchzy7cy7ebT/N4RO1rr0MWlZ5OqWLnJNPT0/H09MRoNMr1cmXolZ/3sTTyHJ3qV2fhkx2sB+N2wZy7QWeAcbvAp742IYUQwhYkH4KZnQAFnt5k9cOvoigMnLGVfeeMPNExhLcHNNUup9CETd21KmzDieQMlu09B8B/+jS69oDLs3Eth0oRJ4QQ/8avqXr2AoqXMiyk0+l49R71fXbhzjOcvZhd3umExqSQE6Xuk7XHsCjQp6kfLYO9rAdjNkHMRtDbQ9f/apJPCCFsTo/X1LMYJ/5Uz2pcoWN9H7o08CHfrPD5X8c1Cii0IoWcKFXRcWn8eSgZvQ5e6d3QelBRin+aDB8B1WqXf0AhhLBF1etBy2Hq9t/X9k69PCu3IjqeI4myglFVIoWcKFUfrVEXcn6wdU0a+LlbD55cD3E7wM4JuryiQTohhLBh3f6rns2I2QSnN1oNNQvy5L4WAShK8fuwqBqkkBOlZsuJFLaduoiDQc/4q5fiUpTinyLbPgkeAeUfUAghbJlXLWijtufi73fV99UrvNy7IXZ6Hf8cu8DO0xc1CCi0IIWcKBWKovDRn+pPgY92qEXNai7WBxxdCYnRYO8KnV8q/4BCCFEZdHkF7Jzh3G44/qfVUB0fVwa3VdcT/3DNUWmUX0VIISdKxZqDSew/Z8TFwcC4HlfdiWoxF18b12EsuPqUf0AhhKgM3P2g/VPq9t//g6uWp3yxZwOc7PXsPZvGusPJ13kBUdncViGXn59PXFwcx44dIzU1tbQzCRtTYLbw8Vq14/iTXepe25Dy0HK4cAQcPaHjcxokFEKISqTTeHD0gOQDcHiF1VANDydGdaoDwMd/HsNskVm5yu6WC7mMjAxmzpxJt27d8PDwICQkhMaNG+Pr60vt2rUZM2YMu3fvLsusooJatjee0xeyqOZiz5gudawHzQVqN3KAjs+Dc7XyDyiEEJWJizdEjFO3/3lffZ+9wtPd6uHpbM+J85lFPT1F5XVLhdxnn31GSEgI3333Hb169WLFihVER0dz/Phxtm/fzuTJkykoKKB3797cc889nDhxoqxziwoiN9/MF4V9i57tXh93J3vrA/YvhtRT4OwNHZ7RIKEQQlRCHZ5VfzC+eAIO/GQ15Olsz7ge9QD4fN1x8grMWiQU5eSW1lrdvXs3mzZtomnT6y/90a5dO0aNGsWsWbP47rvv2Lx5Mw0aNLjusaJyWbDjDAnGXAI8nXg84qq+cAUm2PChut35JXB0v/YFhBBClJyTh3qK9a/JsOEDaP4IGIp/kB4eEcLcLbEkGHNZsjuO4REhmkUVZeuWZuR+/PHHGxZxV3J0dOSZZ55h1KhRdxxMVHyZeQV8teEUcPkCW4P1AXvng/EsuPmrLUeEEEKUnnZPgWsNSDsD0YushpzsDYy7S73xbPrfJ8nNl1m5yqrENztcuHDhhmMHDhy4ozDCtszdEkNqlom6Pq48HF7TejA/BzZ9om53fQUcXK59ASGEELfPwQU6j1e3N32sngW5wqA2NQnycuZ8Rh4Ld54t/3yiXJS4kGvevDmrVq26Zv8nn3xCu3btSiWUqPiMOfl8u/k0AOPvDsXOcNU/pch5kJkEnsHQenj5BxRCiKqgzShw8wNjHEQvsBpytDPwfOGs3MwNJ8k2FVzvFYSNK3EhN2HCBB566CHGjh1LTk4O8fHx9OzZk48++ohFixb9+wuISmHulhjScwtoUMONfs2vWqUhPwe2fK5ud3kZ7ByvfQEhhBB3zt4ZOk9Qtzd9CgV5VsMPhdck2NuZlEwTP2w/o0FAUdZKXMj997//Zfv27WzevJkWLVrQokULHB0d2b9/Pw888EBZZBQVjDE7n7lbYgAY3ysUg15nfcCe7yAzGTxrQctHNUgohBBVSPgT4B4A6ecg6gerIXuDnhfuUm8+nLXxFJl5MitX2dxWQ+D69evTrFkzYmNjSU9PZ/Dgwfj7+5d2NlFBfbvlNBl5BTTyd6dvs6u+76bs4tm4ri+DnUP5BxRCiKrE3ql4Vm7zZ5CfazX8QKsg6vi4cik7n/nbYss/nyhTJS7ktm7dSosWLThx4gT79+9n5syZPP/88wwePJhLly6VRUZRgVzKMvHd1lgAxvdqgP7q2bjI7yDrvDobFzas/AMKIURV1Ho4uAdCejzs/d5qyM6g58We6qzcN5tOk56br0VCUUZKXMjdddddDB48mB07dtC4cWOefPJJoqKiOHv2LM2bNy+LjKICmb35NJl5BTQO8KB3k+vNxn2hbnd9RWbjhBCivNg7qWdBALZcOyvXPyyQer6uGHPy+W5LbPnnE2WmxIXc2rVr+eCDD7C3L248WK9ePbZu3crTTz9dquFExZKaZWJe4bT8S9ebjdszV52N86oFLWU2TgghylWrx8GjJmQkqp0DrmDQ6xjfKxRQL48xZsusXGVR4kKuW7du138hvZ4333zzjgOJiuvrTafINplpFuTB3U38rAdN2bD1C3W763+sOowLIYQoB3aOV83K5VgN92seQEM/dzJyC/h2y2kNAoqycEuF3OLFi2/5BePi4ti6dettBxIVU0pmHt9vU29df6lXKDrd9WbjLqizcWFDNUgohBCClo+p1yhnJqsdBK6g1+t46W71Wrm5W2K4lGW63isIG3NLhdzMmTNp3LgxH330EUeOHLlm3Gg0snr1aoYNG0br1q25ePFiqQcV2vp64yly8s2E1fTkrkY1rAdNWTIbJ4QQFYGdg3qNMqgdBEzZVsO9m/jTJMCDLJOZbzbLrFxlcEuF3MaNG/nwww9Zt24dzZo1w8PDgwYNGtC8eXNq1qxJ9erVGTVqFLVq1eLgwYMMGDCgrHOLcnQ+I5cfdqizcePvvtlsXG2ZjRNCCK21HKa+H2edhz1zrIb0eh0T7lavlZu3NZaUzLzrvYKwIXa3euCAAQMYMGAAKSkpbNmyhTNnzpCTk4OPjw+tWrWiVatW6PW31ZZOVHCzNpwmN99Cq1pedA/1tR40ZcHWL9VtmY0TQgjtGezV9+PfnlPfn9uMtlrvumfjGrSo6cn+c0a+3niK1/s10TCsuFMlrrxefvllvL29efHFF5k4cSJPPvkk4eHhUsRVUsnpuSzceZNr43bPUWfjqoVA2JDyDyiEEOJaYUMKZ+UuXHMHq06n46XCWbnvt5/hfHrudV5A2IoSV19Go5FevXrRoEED3n//fRISEsoil6ggZm44RV6BhTa1q9GlgY/1oMzGCSFExWSwV9e6BvUa5qvuYO0e6kurWl7kFVj4asOp8s8nSk2JC7kVK1YQHx/P2LFjWbJkCbVr16Zv374sXbqU/HzpS1OZJBpzWLTrLAATrndt3O45kJ0C1epAC5mNE0KICiVsKHgGq3ew7rVeg1Wn0/Hy3Q0BWLTrLOczZFbOVt3W+VBfX18mTJjAvn372LlzJ/Xr1+fxxx8nMDCQl156iRMnTpR2TqGBr/45hanAQrs63kTUq249eM1s3C1fbimEEKI82DlA55fU7S2fQ4H1jQ2d6lendS0vTAUWZm+SO1ht1R1d2JaYmMi6detYt24dBoOBe++9lwMHDtCkSRM+//zz0sooNJCcnsuSPXHAja6N+/aK2bjBGiQUQgjxr1o9pq7BmpEAUdfOyj1/l9pXbsGOs6RKXzmbVOJCLj8/n19++YX77ruP2rVr8/PPPzN+/HgSEhKYP38+f/31Fz/99BNTpkwpi7yinMzedBpTgYW2IdXoUNfbetCUDdumqdsyGyeEEBWXnWPxrNzmz6HAuljr3tCXZkEe5OSbmSOrPdikEhdyAQEBjBkzhtq1a7Nr1y727NnDM888g4eHR9ExPXr0wMvLqzRzinKUmmVi4U712rhxPepfOxu3d37xKg4tBmmQUAghxC1rPRzc/CH9HOxbZDWk0+l4roc6Kzd/2xlZg9UGlbiQ+/zzz0lISGDGjBm0bNnyusd4eXkRExNzp9mERuZuiSEn30zzIE+6Xd03Lj+3+Nq4zhPkTlUhhKjo7J2g04vq9uZPwWxdrPVu4kdDP3cy8wqYvz22/POJO1LiQu7xxx/HycmpLLKICsCYk8/8bbHADWbjohdARiJ4BKndw4UQQlR84U+Aqy+knYX9S6yG9Hod4+6qD8DcrTFk5hVoEFDcLuniK6z8sD2WjLwCQv3c6N3Ez3qwwARbvlC3O41Xr70QQghR8Tm4QMcX1O1Nn4DZuljr1zyAuj6upGXns6BwSUZhG6SQE0Wy8gqYs0U9JT6uR330+qtm4/YvBmMcuPlB68c1SCiEEOK2tR0NLtXhUgwcXGo1ZNDreLaHOiv37ebT5JjMWiQUt0EKOVFk0c6zXMrOJ6S6C/2aB1gPmgvUaysAOj4P9s7lH1AIIcTtc3BV378BNn0MFuti7f6WgdSs5kxKpokfC5vBi4pPCjkBQG6+mW82q7eej+1eDzvDVf80Di6FS7HqT3NtRpV/QCGEEHeu7ZPgXA0unoRDy62G7A16nu2uzsp9vekUeQUyK2cLpJATAPy8J44LGXkEejrxQKua1oMWs3pNBUDEOPWnOiGEELbH0V19HwfY+NE1s3IPhQfh7+FEcnoeP+85p0FAUVJSyAnyzRZmbVRn457uVg8Hu6v+WRz+FS6eACcvaDum/AMKIYQoPe2eAidPSDmmvr9fwdHOwNPd6gIwc8Mp8s0WLRKKEpBCTrA8Kp74tBx83BwZ3DbYetBiKZ6N6zAWnDyufQEhhBC2w8kTOjyrbm/6WH2fv8LQdrXwcXMgPi2H5VHxGgQUJSGFXBVntijM3HAKgDFd6uBkb7A+4NhqOH8IHNyh/dMaJBRCCFHq2j8Njh5w/jAcXWk15GRvYEwXdVbuq39OYrYoWiQUt0gKuSpu1YFEYlKy8HKx59EOta0HFQU2faRut39KvUBWCCGE7XOupp5iBdj8ifp+f4XHOtTGy8We2IvZrNyfoEFAcas0L+RmzJhBSEgITk5OtG/fnl27dt30+LS0NMaNG0dAQACOjo6EhoayevXqckpbuVgsCjP+PgnAqE51cHO0sz7gxDpI3Af2rtBhnAYJhRBClJkOz4K9i/o+f3K91ZCrox2jO9UBYPrfJ7HIrFyFpWkht2TJEiZMmMDkyZPZu3cvYWFh9OnTh/Pnz1/3eJPJxN13301sbCxLly7l2LFjzJ49m6CgoHJOXjn8dSSZY8kZuDnaMSIixHrwytm4tqPAtXq55xNCCFGGXK9oJ7Xp42tm5UZ0CsHdyY4T5zNZezhJg4DiVmhayH322WeMGTOGkSNH0qRJE2bNmoWLiwtz58697vFz584lNTWVFStW0KlTJ0JCQujWrRthYWHlnNz2KYrC9H/U2bjhEbXxdLG3PuD0Bji3G+ycIOL58g8ohBCi7EU8BwYHiNsBZ7ZaDXk42Rf9kD9zwykURWblKiLNCjmTyURkZCS9evUqDqPX06tXL7Zv337d5/z2229EREQwbtw4/Pz8aNasGe+//z5m842bFubl5ZGenm71ELD5RAr7zxlxstczunOdaw/Y9LH6a+sR4O537bgQQgjb5xEArR5Tty93KLjCE51CcLTTs++cke2nL5ZzOHErNCvkUlJSMJvN+PlZFwl+fn4kJV1/Cvf06dMsXboUs9nM6tWrefPNN/n000/53//+d8OvM3XqVDw9PYsewcHBNzy2KpleeG3csHa1qe7maD0Yu1X9yczgAJ1e1CCdEEKIctPpRdAZ4PQ/EB9pNeTj5sigNurn5uV+o6Ji0fxmh5KwWCzUqFGDb775hvDwcAYPHszrr7/OrFmzbvicSZMmYTQaix5xcXHlmLhi2hWTyq7YVBwMep7qWvfaAy7PxrV8FDzl+kMhhKjUqoVAi0Hq9qZPrxke06Uueh1sOn6BQwnG8s0m/pVmhZyPjw8Gg4Hk5GSr/cnJyfj7+1/3OQEBAYSGhmIwFPc6a9y4MUlJSZhMpus+x9HREQ8PD6tHVff1RrVv3EPhQfh7OlkPxkeqP5XpDNB5fPmHE0IIUf46TwB0cGwVJB+yGqpV3YV+LQIB+Fpm5SoczQo5BwcHwsPDWb+++JZni8XC+vXriYiIuO5zOnXqxMmTJ7Fc0YX6+PHjBAQE4ODgUOaZK4PjyRmsP3oenY6iho9WNn+m/tpikPpTmhBCiMrPNxSaDFC3L38OXOHpwrM3K/cnEJeaXZ7JxL/Q9NTqhAkTmD17NvPnz+fIkSOMHTuWrKwsRo4cCcDw4cOZNGlS0fFjx44lNTWVF198kePHj7Nq1Sref/99xo2THme36ptN6k9TfZr4U9fXzXrw/NHiDt+dxpdvMCGEENrq8or666FlcPGU1VCzIE+6NPDBosDszTIrV5FoWsgNHjyYTz75hLfeeouWLVsSHR3NmjVrim6AOHv2LImJiUXHBwcH8+eff7J7925atGjBCy+8wIsvvsjEiRO1+iPYlERjDr9Gq+vmXV4U2crWL9RfG90HNRqVXzAhhBDaC2gBDfqAYoEt187Kje1WD4Cf9sRxMTOvvNOJG9ApVawxTHp6Op6enhiNxip3vdz7q4/wzabTtKvjzU9PX3X6+tIZ+L9WoJhhzN8QFK5NSCGEENqJ2wVz7ga9HbwQDV7FnR4UReH+GVvZf87IC3fVZ0LvhtrlFEVs6q5VcfuMOfks2nkWgGeuNxu37f/UIq5udynihBCiqgpuByFdwFKgfi5cQafT8UzhrNz87WfIyivQIqG4ihRyVcSinWfJzCsg1M+N7qE1rAczkmHvD+p2l5fLP5wQQoiKo2vhtXJ7v4dM6yUz+zT1p46PK8acfBbvlnZeFYEUclVAXoGZuVtjAHiqaz30ep31ATu+AnMe1Gyr/iQmhBCi6qrTDYLaQEEubJ9uNWTQ64o6HszZfJp8s+V6ryDKkRRyVcCKqHguZOQR4OnEgLBA68GcS7B7jrrd5WXQ6a59ASGEEFWHTgdd/6Nu756jfk5c4cHWQfi4OZJgzOW36AQNAoorSSFXyVksCl8XthwZ3bkODnZXfct3fQumDKjRRL1bSQghhAjtAzWagilT/Zy4gpO9gVGdQwD4etMpLJYqdc9khSOFXCX315FkTl/Iwt3JjiHtalkPmrJg50x1u/ME0Ms/ByGEEKizcp1fUrd3zgSTdRPgR9vXxs3RjuPJmfxz7Px1XkCUF/nkrsQURWFW4XJcj3dQ/9NZ2fs9ZF9UV3Bo+kD5BxRCCFFxNX0AvGqrnxNRP1gNeTrb82h7dXLg8ueM0IYUcpXYnjOX2Hs2DQeDnic6hVgPFphg2zR1u9N4MNhd/XQhhBBVmcEOOr2gbm+bBuZ8q+FRnevgYNCzO/YSkWdSNQgoQAq5Su3rwp+SHgoPooa7k/Xg/iWQHg9u/tBymAbphBBCVHgtHwPXGmCMgwNLrYb8PJx4oFUQADM3yLJdWpFCrpI6kZzBX0fOo9PBk12uagBsMcOWz9Xtjs+BnWP5BxRCCFHx2TtBxLPq9pbPwWLdbuSpbnXR6dTrsU8kZ2gQUEghV0l9U3inau8mftTzdbMePPwrpJ4CJy8IH1n+4YQQQtiONqPA0QNSjsGx1VZD9Xzd6N1EXR99zpYYLdJVeVLIVUJJxlxWRMcD8HThcipFFAU2Fy6G3P4ZcLyqyBNCCCGu5OQJbZ9Ut7d8pn6OXOFyg+BlUfGkZOaVd7oqTwq5Sui7rTHkmxXahXjTulY168GTf0HyAbB3hfZPaxNQCCGEbekwFuycID4SYjdbDYXXrkZYsBemAgsLd5zVKGDVJYVcJZOZV8CiXep/pKe61r32gM2fqr+2GQku3uWYTAghhM1yqwGtHlO3L19jXUin0zG6cx0AftgRS26+ubzTVWlSyFUyP++JIyO3gLo+rtzVqIb14JltcHY7GBwg4jltAgohhLBNHZ8HnQFO/Q0JUVZDfZv5E+jpREqmSZbtKmdSyFUiZovCd1tjARjZuQ56/VXrpl7+KarlMPAIKN9wQgghbFu1EGj2kLq95QurIfsr+pXO2RKDosiyXeVFCrlK5K8jyZxNzcbT2Z6HWgdZDyYfghNrAR10fEGTfEIIIWxc5/Hqr4d/hZSTVkOD29bC1cHAseQMtpxMKf9sVZQUcpXInM3qrd+Ptq+Fi8NVKzVs/VL9tckAqH7VnaxCCCHErfBrCqH3AAps/cJqyNPZnkfaBAPw7WZpRVJepJCrJA6cM7IrNhU7vY7hESHWg2lniztydxpf3tGEEEJUJp0nqL/uWwzp1tfDjepUB50ONh6/IA2Cy4kUcpXEnC1qA+D7WgTg73nVclzbZ4BihjpdIai1BumEEEJUGrXaQ+1OYMlXP1+uHKruQp8m/gDM3SqzcuVBCrlKIMmYy8r9iQCM7nxVy5HsVNj7vbrd+aVyTiaEEKJSuvx5suc79XPmCqO7qK1Iftkbz0VpEFzmpJCrBOZvj6XAotCujjfNa3paD+76BvKzwb8F1O2hTUAhhBCVS/1e4Ncc8rNg12yroTa1qxFW0xNTgYUF0iC4zEkhZ+OyTQUs2qn+R7nckLGIKQt2fq1udx4PuqvakQghhBC3Q6crvoN119dgyr5iSMfowmW7pEFw2ZNCzsb9EnkOY04+tau70Kuxn/Vg1ALISVV7/zS+X5N8QgghKqkmA8GrNmRfhOiFVkN9m/kTcLlB8D5pEFyWpJCzYRaLwtzLDYA7hmC4sgGwOR+2TVe3Oz4PBrtrX0AIIYS4XQY79fMFYNs0MBcUDdkb9DzRMQRQW2NJg+CyI4WcDfvn2HliUrJwd7Ir6t1T5NByMJ4FV19o+ag2AYUQQlRuLR8Fl+qQdgYOr7AaGtKuFi7SILjMSSFnwy43XBzWrhaujlfMuClK8fIp7Z8Ge+fyDyeEEKLyc3CBdk+r21u/VD9/Cnk62zOocJJhzhZpRVJWpJCzUYcSjGw/fRGDXseIwunrIifWwflD4OAGbZ/UJJ8QQogqot0YsHeBpP1weoPV0MhOIeh0sOGYNAguK1LI2ai5W2IB9YLSQK+rZtwuL5sS/gQ4VyvPWEIIIaoaF29oPVzdvmrZrtrVXendRL0RTxoElw0p5GzQ+fRcftsXD8CTXa5qABy3G85sBb09dHhWg3RCCCGqnA7Pgs6gzsglRFsNXf6cWiYNgsuEFHI26IcdZ8g3K4TXrkbLYC/rwcs/DbUYBJ5B5R1NCCFEVVStNjR7UN3e9n9WQ21qV6NFTU/yCiws3CkNgkubFHI2JjffzIIdZwB48uoGwBeOw9FV6nanF8s5mRBCiCrt8ufOoeWQWnwaVafTFTWs/367NAgubVLI2ZjlUfFcys6nZjVnejf1tx7c9iWgQMN7wbehJvmEEEJUUf7NoV5PUCywfYbV0L3NA4oaBP8uDYJLlRRyNkRRFOZviwVgRMRVDYDTE2DfEnW70/hyzyaEEEIUzcpFLYCs4t5x9gY9j0fUBuD77WekQXApkkLOhuyMSeVoUgbO9oai3jxFdswESz7UioBa7bUJKIQQomqr0xUCW0FBDuz6xmpoSNtaONjpORBvJCouTZt8lZAUcjZkXuFyXA+0DsLTxb54IDcdIuep23JtnBBCCK3odMWfQ7u+AVNW0ZC3qwMDwgIBis4uiTsnhZyNiE/LYe3hJEA9rWolch7kpYNPKDToU+7ZhBBCiCKNB0C1OpBzST3FeoXL66+uPpDI+YxcDcJVPlLI2YgFO85gUSCibnUa+rsXDxSY1NOqoC5erJdvqRBCCA3pDernEcC26WDOLxpqFuRJ61pe5JsVftwZp1HAykU+9W1Abr6ZxbvU3jtPdAqxHjz4C2QkgJsftBhc/uGEEEKIq7UcBi4+YDyrtiO5wuVlJRfuPEO+2aJBuMpFCjkb8Ft0Apey8wnycqZXY7/iAUWBbdPU7fZPg52jNgGFEEKIK9k7Q/tn1O1t/6d+XhXq2ywAX3dHzmfkseZgkkYBKw8p5Co4RVGYV3hR6OMRta1bjpxcD+cPgb0rtBmlTUAhhBDietqOBnsXSDoAMRuLdjvY6RnWrhYgNz2UBinkKrg9Zy5xODEdRzs9g69uObLtS/XX8BHgXK38wwkhhBA34uINrR5Tt7daL9v1aPta2Ol17DlziYPxRg3CVR5SyFVwl2fjHmgVRDVXh+KBhGiI2aQuUtxhrCbZhBBCiJvq8Czo9HBqPSQdLNpdw8OJvs0DAHXZLnH7pJCrwBKNOUXXD1y+OLTI5UWJmz0EXrXKN5gQQghxK7zrqO1IALZPtxp6oqO60sOv0QlcyjKVd7JKo0IUcjNmzCAkJAQnJyfat2/Prl27bul5ixcvRqfTMXDgwLINqJGFO85itii0q+NN4wCP4oFLscV3AXV6QZNsQgghxC25/Dl14Gcwxhftbl2rGk0DPcgrsLBkj7QiuV2aF3JLlixhwoQJTJ48mb179xIWFkafPn04f/78TZ8XGxvLK6+8QpcuXcopafnKzTfz4+WWI1fPxm3/Sl2UuG4PdZFiIYQQoqIKCofancBSADtnFe3W6XRFZ5t+2H4Gs0XWX70dmhdyn332GWPGjGHkyJE0adKEWbNm4eLiwty5c2/4HLPZzKOPPso777xD3bp1yzFt+Vm1P5GLWSYCPJ3o3eSKliPZqRD1g7ots3FCCCFsweUGwZHz1GUlCw0IC6Saiz3xaTmsP5KsTTYbp2khZzKZiIyMpFevXkX79Ho9vXr1Yvv27Td83pQpU6hRowajR4/+16+Rl5dHenq61aOiu7LlyGMdamNnuOLbtHsO5GerM3F1e2gTUAghhCiJBn3UZSTz0mHv90W7newNDG6rXuf9/fYzWqWzaZoWcikpKZjNZvz8/Kz2+/n5kZR0/SaBW7ZsYc6cOcyePfuWvsbUqVPx9PQsegQHB//7kzS292waB+KNONjpGdruihsZ8nNh19fqdscX1MWJhRBCiIpOr4eI59TtHTOtlu16rEMt9DrYcjKFk+czNApouzQ/tVoSGRkZPP7448yePRsfH59bes6kSZMwGo1Fj7i4in9B5Q+Ft2IPCAvE+8qWI/t+hKwL4FETmj6gTTghhBDidrQYDK41IP2c1bJdNau5FK1aJLNyJadpIefj44PBYCA52fq8eHJyMv7+/tccf+rUKWJjY+nfvz92dnbY2dnx/fff89tvv2FnZ8epU6eueY6joyMeHh5Wj4osJTOP1QfU2cjhEbWLByyW4lu3I54Fg70G6YQQQojbZO8E7Z9St7daL9t1+aa+XyLPkZGbf50nixvRtJBzcHAgPDyc9evXF+2zWCysX7+eiIiIa45v1KgRBw4cIDo6uugxYMAAevToQXR0tE2cNv03P+2Jw2S2EFbTkxY1vYoHjq2GiyfB0RNaD9csnxBCCHHb2hQu25V8AE5vKNodUa86DWq4kWUy80vkOe3y2SDNT61OmDCB2bNnM3/+fI4cOcLYsWPJyspi5MiRAAwfPpxJkyYB4OTkRLNmzaweXl5euLu706xZMxwcHG72pSo8s0Vh0U615chjHWpbD16ejWszEhzdyzmZEEIIUQpcvKHV4+r2tuJlu3Q6HcMLZ+W+334Gi7QiuWWaF3KDBw/mk08+4a233qJly5ZER0ezZs2aohsgzp49S2JiosYpy8fG4+c5dykHT2d7+ocFFg/E7Yaz20FvD+2f0S6gEEIIcaciLi/b9bfVsl0PtgrC3dGO0ylZbDmZomFA26JTFKVKlb3p6el4enpiNBor3PVyI7/bxT/HLjCmSx1e79ekeOCn4XD4VwgbBg/M1C6gEEIIURp+fkK94aHFEHjw66Ld7/x+iO+2xtKzUQ3mPNFWu3w2RPMZOaGKS81mw/ELAAxrf8Vp1dQYOPK7ut3xOQ2SCSGEEKXscoPgg0utlu16vPCyor+PnefsxWwtktkcKeQqiIU7z6Io0KWBD3V8XIsHdsxUl+Oq1xP8mmoXUAghhCgtQeFQu/M1y3bV9XWja6gvigKLCpepFDcnhVwFkJtv5qfCBYMfv/Imh+xUiFqgbstsnBBCiMrkBst2PdZebYT/05448grMGgSzLVLIVQB/HEwkNctEoKcTdzWqUTwQ+R3kZ4FfM1mOSwghROXSoPcVy3bNL9p9V6MaBHg6kZplYs3B66/yJIpJIVcB/FDYyXpou1rF66oW5MHOb9TtiOdkOS4hhBCVi15fPCt3xbJddgY9QwrXX124U06v/hsp5DR2KMHI3rNp2Ol1DG53RUPjA0shMwncA6DZQ9oFFEIIIcpK80GFy3bFw8FfinYPbhuMQa9jV0wqJ5Jl/dWbkUJOYwt2qD9t3NPMnxruTupORSluANz+abCz7UbHQgghxHVduWzX9ulFy3b5ezrRq7F6qZHMyt2cFHIaSs/NZ0WUetu11U0Op9bD+cPg4AbhIzVKJ4QQQpSDNqPBzhmSDkDMpqLdjxa24vpl7zlyTHLTw41IIaehZZHnyMk3E+rnRrs63sUD26apv7YeDs5emmQTQgghyoWLN7R6VN2+fDYK6Fzfh1reLmTkFvD7/gSNwlV8UshpRFEUFlyxrqru8s0MSYULCev0shyXEEKIqqHDs4AOTqyFC8cA0Ot1DCtsRbJwxxkNw1VsUshpZMfpVE6ez8TFwcADrYKKB7YV/jTSZCBUq33d5wohhBCVSvV60PBedXv7jKLdj4TXxMGgZ985IwfOGTUKV7FJIaeRBYU/XTzQKgh3J3t1Z3qCulwJSANgIYQQVcvlz719iyFTXbKyupsjfZv7A7Bol8zKXY8Uchq4kJHHn4fUJoePXrmu6s6v1eVKanVUly8RQgghqopaERDYGsx5sPvbot2XPyd/jU4gPTdfq3QVlhRyGvg5Mo4Ci0KrWl40CfRQd+Zlqis5gMzGCSGEqHp0OogYp27v/hbycwBoG1KNBjXcyDaZ+bWw04MoJoVcObNYFBbvUtdVHdquVvFA9ELINYJ3XQjtq1E6IYQQQkNNBoJnMGSnwP4lAOh0Oh5tX7zSg1LYa06opJArZ1tPpXA2NRt3Jzv6twhUd1rMsOMrdbvDs+qyJUIIIURVY7Ar7tiwfQZYLAA80LomTvZ6jiZlsPfsJQ0DVjxSMZSzH3epLUceaBWEs4NB3XlsNVyKBedq0HKYduGEEEIIrbUeDg7ukHIcTv4FgKezPQPC1MmPhTtkpYcrSSFXjs5n5LL2UDJAUW8coLjlSJtR4OCqQTIhhBCignDygPAR6vb2aUW7L9/0sPJAIpeyTFokq5CkkCtHSyPPFd3k0Mi/8CaHc3sgbgfo7aHdU9oGFEIIISqC9s+AzqAu2ZW4H4CwYC+aB3liKrCwNPKcxgErDinkysmVNzkMu/Imh8vLkTR/BNz9NUgmhBBCVDBewdB0oLp9xbJdl296WLTrLBaL3PQAUsiVmytvcrjv8k0Ol87A4V/V7cu3XAshhBCi+HPx4C9qw3ygf1gg7o52xKRksf30RQ3DVRxSyJWT697ksPNrUCxQtzv4N9MunBBCCFHRBIWrDfItBernJeDqaMcDrdVlLRfulJUeQAq5cnHdmxxyjbD3e3U74nmNkgkhhBAV2OUG+ZHfqY3zKf4cXXsomfMZuVolqzCkkCsH173JYe/3YMoA30ZQv6e2AYUQQoiKKLSv2ig/1whRCwBo5O9BeO1qFFgUfomUlR6kkCtj173JwVwAO2ap2x2eVZclEUIIIYQ1vV79nAS1cb7FDMDgtsEALNktKz1IIVfGrnuTw+EVkH4OXHygxWBN8wkhhBAVWstH1Yb5aWfg6EoA7msRgJujHbEXs9lxOlXjgNqSQq6MLdqp3uTw4OWbHBSl+FbqdmPA3knDdEIIIUQF5+ACbUar29tnAODiYMeAlurkyOLdVXulBynkytD5jFzWHVZvchh6+SaHszsgIQoMjtD2SQ3TCSGEEDai3Ri1cX7cTrWRPjCk8PTqHweTSMuuuis9SCFXhi7f5ND6ypscLs/GhQ0BVx/twgkhhBC2wt0fmj+sbhfOyjUP8qRxgAemAgsroqruTQ9SyJWRK29yGHr5JofU03B0lbp9+eJNIYQQQvy7y5+bh3+FtDh0Oh1D26mzcot3x1XZmx6kkCsj173JYefXgAL1e0GNRprmE0IIIWxKQAsI6QKKGXapDYLvDwvC0U7P0aQM9p0zahxQG1LIlZElu9XZuIEtC29yyEkr6oEjs3FCCCHEbYi43CD4e8jLwNPFnnubBwBqK5KqSAq5MnApy1S0ksPlXjdqA+BM8G0M9e7SMJ0QQghhoxr0hur1Ic8IUQuB4psefotOICuvQMt0mpBCrgysiI7HZLbQJMCDZkGeagPgXd+ogxHSAFgIIYS4LXo9dBirbu+cCRYz7ep4U8fHlSyTmZX7E7TNpwEp5EqZoihFp1WLZuOO/AbGOLUBcPNBGqYTQgghbFzYULVB8KVYOLYanU5X9Hm7uPDztyqRQq6UHYg3cjQpAwc7PQNbBqk7C2+Vpu2T0gBYCCGEuBMOrhA+Ut0u/Hx9qHVN7PQ6os6mcSwpQ8Nw5U8KuVJ2eTbunqb+eLrYQ9wuiN8DBgdoO1rjdEIIIUQl0O4ptUHw2e0QH4mvuyO9GvsBVW+lBynkSlGOycxv0er5+aLTqpcbALcYBG41NEomhBBCVCIeAdDsQXV7+1cADC7sKbc8Kp7cfLNWycqdFHKl6I+DiWTkFRDs7UxE3epw6Qwc+V0dlJYjQgghROkpahC8Aozn6NrAl0BPJ9Ky8/nzUJKm0cqTFHKl6PJp1UfCg9HrdWoDYMUCdXuAX1ON0wkhhBCVSGBLtUGwRe0MYdDreKSNOiu3pArd9CCFXCmJTcliZ0wqOh08HF4TctPV3nEAEeO0DSeEEEJURpdn5SLnQV4mj7SpiU4H205d5MzFLE2jlRcp5ErJT3vU6r9rA18CvZzVVRxMGeATCvV6apxOCCGEqIRC7wHvupBrhOhF1KzmQpcGvkDVmZWTQq4UFJgtLI08BxTe5GAxq40KQf1pQS9/zUIIIUSp0+uLZ+UKGwQPLbzZ8OfIcxSYLRqGKx8VosKYMWMGISEhODk50b59e3bt2nXDY2fPnk2XLl2oVq0a1apVo1evXjc9vjxsPH6B8xl5eLs6qLc/H10JaWfB2RvChmiaTQghhKjUWg4DJy9IPQ3H19CzsR/VXR24kJHH30fPa52uzGleyC1ZsoQJEyYwefJk9u7dS1hYGH369OH8+ev/5W/YsIGhQ4fyzz//sH37doKDg+nduzfx8fHlnLzY5enbB1oF4WCnL24A3GYU2DtrlksIIYSo9BxcIfwJdXv7VzjY6XkovCZQfNlTZaZTFEXRMkD79u1p27Yt06er/dYsFgvBwcE8//zzTJw48V+fbzabqVatGtOnT2f48OH/enx6ejqenp4YjUY8PDzuOP+FjDwipq6nwKKw9qWuhOYfh2/vUhsVvnQQ3P3v+GsIIYQQ4iaM8fBlC/UO1qc3cdJQl16fbcKg17FjUk983R21TlhmNJ2RM5lMREZG0qtXr6J9er2eXr16sX379lt6jezsbPLz8/H29r7ueF5eHunp6VaP0rRs7zkKLAotg70I9XOHHYWzcc0fliJOCCGEKA+eQdBkoLq9Yyb1a7jTMtgLs0VhRZR2Z+zKg6aFXEpKCmazGT8/P6v9fn5+JCXdWjO/V199lcDAQKti8EpTp07F09Oz6BEcHHzHuS9TFIUlhdO2g9sGQ1ocHFqhDkoDYCGEEKL8XP7cPbAUMpLUVmDA0shzaHzysUxpfo3cnfjggw9YvHgxy5cvx8np+ovRT5o0CaPRWPSIiyu98+WRZy5x+kIWzvYG7msRALu+AcWsNigMaFFqX0cIIYQQ/6JmOAS3B0s+7P6W/mGBONjpOZacwcH40j0bV5FoWsj5+PhgMBhITk622p+cnIy//81PS37yySd88MEHrF27lhYtblw0OTo64uHhYfUoLZdvcujXIgB3XR5EzlcHpAGwEEIIUf4uz8rtmYunXQF9mqq1xM+RlfemB00LOQcHB8LDw1m/fn3RPovFwvr164mIiLjh8z766CPeffdd1qxZQ5s2bcoj6jUy8wpYdSARKDytuu9HyDOqjQkb9NEkkxBCCFGlNboPPGtB9kXY/xOPFJ5e/TU6gbwCs8bhyobmp1YnTJjA7NmzmT9/PkeOHGHs2LFkZWUxcuRIAIYPH86kSZOKjv/www958803mTt3LiEhISQlJZGUlERmZma55l65L4Fsk5m6vq60qeUJOwobALcfKw2AhRBCCC0Y7KD90+r2jpl0qlcdfw8njDn5/HW4cvaU07ziGDx4MJ988glvvfUWLVu2JDo6mjVr1hTdAHH27FkSExOLjp85cyYmk4mHH36YgICAoscnn3xSrrkv3+QwqE0wuhPrIPUUOHqqjQmFEEIIoY3Wj4ODG1w4giHmHx5sHQTA0kp6elXzPnLlrTT6yJ08n0mvzzZi0OvYPukuaix7BGI2Qcfnoff/SjmxEEIIIUrkj1dh5yyo34vTfeZz16cb0etgx6Se1PC4/s2RtkrzGTlb9MtedV3V7qG+1Mg6qRZxOgO0e1rjZEIIIYRQT6/q4ORf1CWe8NrVsCiwrBL2lJNCroTMFoVlhYXcw+E1i6+NazIAvEqvR50QQgghbpN3XWjUT93eMbPopofK2FNOCrkS2noyheT0PDyd7bmrlg4O/KQOSANgIYQQouLoMFb9dd9i+jVwxMlez8nzmUTHpWkaq7RJIVdCl0+rDggLxDFqHphNENQGgttpG0wIIYQQxWp3Av8WUJCD+4EfuKewp9zSyHMaBytdUsiVQHpuPmsOqkuHPRLmA7u/VQcuV/1CCCGEqBh0uuIG/bu/ZVArtRvGb/sSyM2vPD3lpJArgdX7E8krsFC/hhvN0/6CrAvgEQRN7tc6mhBCCCGu1vRBcPODjEQ65G4myMuZjNwC1h5O/vfn2ggp5Erg8nTsw62D0F2+yaHdU2Cw1zCVEEIIIa7LzgHajgFAv+MrHmoVCFSu06tSyN2i2JQs9py5hF4Hg3xiIfkg2LtA+AitowkhhBDiRtqMAjsnSIxmWEACAJtPXCDRmKNxsNIhhdwtunyTQ5cGvnjvL7w2ruUwcK6mYSohhBBC3JRrdWgxGAD/I3NpF+KNosCyvZWjp5wUcrfAYlGKvuHDGxbA8TXqQPtnNEwlhBBCiFty+abEo6sY0UTd/KWS9JSTQu4W7Dh9kfi0HNyd7Oh2aRmgQIM+4NNA62hCCCGE+Dc1GkO9u0CxcHfmbzjbGzidksXes5e0TnbHpJC7BUsvr+TQ1B27fYvUndJyRAghhLAdhY37HfYt4IEmnkDluOlBCrl/kZlXwB8H1N5xo503QX4W1GgKdbtrG0wIIYQQt65eT6jeAPLSGeOxHYDf9yWSY7LtnnJSyP2LPw4kkpNvpl51J4JO/KDu7DBWbTQohBBCCNug10MH9dr2kJPfE+zlSGZeAX8eStI42J2RQu5fXL5b9ZVax9EZz4GLDzR/RONUQgghhCixsKHg5IXuUgz/qRMD2P7pVSnkbiIuNZsdp1PR6eAu4zJ1Z9vRYO+kbTAhhBBClJyDK4Q/AUDvjOUAbD2VQnya7faUk0LuJi63HHksOAXHhF2gt4c2ozVOJYQQQojb1m4M6Aw4ndvK4OA0taecDc/KSSF3A4qiFJ1WHeOwVt3Z/GFw99MwlRBCCCHuiGfNojXSxzqtA9TuFLbaU04KuRvYHXuJs6nZ1HEwEpwgDYCFEEKISqOwFUnthFUEO2Ry5mI2u2Nts6ecFHI3sDQyDoA3/LahsxRA7U4Q2FLbUEIIIYS4c8FtIagNOrOJN/13APDznjiNQ90eKeSuI9tUwOoDSTiRR9f0lepOaQAshBBCVB4R6qxc9/TfcCCfPw4mkZtvez3lpJC7jj8PJZGZV8Aoj13Y510Cr1rQ8F6tYwkhhBCitDQeAB5BOOSmMNx9D5l5Baw7nKx1qhKTQu46fomMBxRG211xbZzeoGkmIYQQQpQig716Byswxv5PQGFFVLy2mW6DFHJXSUjLYeupFDrrD1I9OwYc3KDVY1rHEkIIIURpaz0C7Jzxyz5Oe91RNh6/wMXMPK1TlYgUcldZHhWPosAE97/UHa0eAydPbUMJIYQQovS5eEPLoQCMd/uLAovCyv2JGocqGSnkrqAoCsuj4qmrS6B13m5AB+2e0jqWEEIIIcpKe/Vmxg75OwjWJbPcxk6vSiF3hUMJ6Zw8n8lo+8IGwA37QvV62oYSQgghRNnxDYX6d6NDYZTdn0THpXH6QqbWqW6ZFHJXWB4VjweZPGzYpO6QliNCCCFE5Vf4eT/EbiPuZLMiOkHjQLdOCrlCBWYLv+1LYIjhHxyVXPBrBiFdtI4lhBBCiLJW7y7waYizksMjho2siIq3mSW7pJArtO3URVIzshl5+bRqh2dBp9M2lBBCCCHKnk5XNCv3hN1azqVmsvesbSzZJYVcoRVR8fTR7yaAi+DqC80e0jqSEEIIIcpLi8HgXI1aumR66veybK9t3PQghRzqklxrDiUx6nID4Dajwd5J21BCCCGEKD8OLhD+BACjDGtYuT8RU4FF20y3QAo5YN3hZBrkH6ON/jiKwQHajNI6khBCCCHKW9sxKDoDEYbDBOWe4J9j57VO9K+kkAOW7Y1nZOFsnK7ZQ+Dup3EiIYQQQpQ7zyB0TQcCMNKwxiaW7KryhdyFjDyOnzhGP/1OdUf7Z7QNJIQQQgjtdHgWgAGGbUQfOY4xJ1/jQDdX5Qu53/cl8KhhHfY6M9TuBIEttY4khBBCCK3UbAM12+KoK2AQ61h9oGIv2VXlC7nVUacYZliv/kYaAAshhBCisB54zG4dv++N0TjMzVXpQu7k+UzqJ/2Bty4Ts0ctaHiv1pGEEEIIobXGAzC7BeKrSyfg7GriUrO1TnRDVbqQ+zXqHKMMfwBgiHgG9AaNEwkhhBBCcwZ7DO3HADDK7g9+i664Nz1U2UJOURTiIlcTqo+nwM4FWj2mdSQhhBBCVBThT1Cgd6Kp/gwndq+tsEt2VdlCLursJfrn/Kb+puVj4OSpbSAhhBBCVBwu3lhaDAbgnszlHIxP1zjQ9VXZQm7r7t30NERhQYddhLQcEUIIIYQ1h45qK5Le+j38vWOnxmmur8oWcgEnFgFwKeguqF5P4zRCCCGEqHBqNOKifxf0OgWfQ/MpMFe8JbuqbCF3r7IZAK+7XtA4iRBCCCEqKs8eap0wwLKebUcqXiuSClHIzZgxg5CQEJycnGjfvj27du266fE///wzjRo1wsnJiebNm7N69eoSf00XnYnzzvUw1O12u7GFEEIIUcnZNejFBcfauOtyuLDpO63jXEPzQm7JkiVMmDCByZMns3fvXsLCwujTpw/nz19/odpt27YxdOhQRo8eTVRUFAMHDmTgwIEcPHjwlr6eMSunaLug7TOg05XKn0MIIYQQlZBeT2642oqkTfJPZObkaRzImk7R+H7a9u3b07ZtW6ZPnw6AxWIhODiY559/nokTJ15z/ODBg8nKymLlypVF+zp06EDLli2ZNWvWv369P3+cxj3DXuDMxECCp5xEZ+9cen8YIYQQQlQ6Sl4mmVNDcSeLbW2n0bHfcK0jFbHT8oubTCYiIyOZNGkSiqKQkZEBQNeuXdm0aRPPPvvsNc/ZunUrzz33HOnpxbcBd+/enZUrV1rtuywvL4+8vOLq2SFKnRY94NMPr5x8qOCL4QohhBBCe3ur96d1wo/Y7ZpFepeB5fI13d3d0f3LmUNNZ+QSEhIICgpi27ZtNG3aFE9P6eUmhBBCCAFgNBrx8PC46TGazshdyd3dHaPRCMCbb77J1q1b+fvvv685rnr16syaNYtHHnmkaN/s2bP54IMPOHXq1DXHXz0jl5iYSLt27Th8+DBBQUFl8CcRpSE9PZ3g4GDi4uL+9R+x0I58nyo++R7ZBvk+2Ya0S6nUDqlTbt8nd3f3fz1G00LOx8cHg8FAcnIyOp2u6C8lLS2NoKCg6/4lBQQEkJGRYTWWnp5OYGBgif5S3d3d5T+LDfDw8JDvkw2Q71PFJ98j2yDfJ9tQkb5Pmt616uDgQHh4OOvXry/aZ7FYWL9+PREREdd9TkREhNXxAOvWrbvh8UIIIYQQlZXmp1YnTJjAiBEjaNOmDe3ateOLL74gKyuLkSNHAjB8+HCCgoKYOnUqAC+++CLdunXj008/pV+/fixevJg9e/bwzTffaPnHEEIIIYQod5oXcoMHD+bChQu89dZbJCUl0bJlS9asWYOfnx8AZ8+eRa8vnjjs2LEjixYt4o033uC1116jQYMGrFixgmbNmt3S13N0dLT6VVRMjo6OTJ48Wb5PFZx8nyo++R7ZBvk+2YaK+H3SvI9ceUtPT8fT0/OW7gQRQgghhKjINF/ZQQghhBBC3B4p5IQQQgghbJQUckIIIYQQNkoKOSGEEEIIG1UpC7kZM2YQEhKCk5MT7du3Z9euXTc9/ueff6ZRo0Y4OTnRvHlzVq9eXU5Jq7aSfJ9mz55Nly5dqFatGtWqVaNXr17/+n0VpaOk/58uW7x4MTqdjoEDB5ZtQFHi71FaWhrjxo0jICAAR0dHQkND5X2vHJT0+/TFF1/QsGFDnJ2dCQ4O5qWXXiI3N7ec0lY9mzZton///gQGBqLT6VixYsW/PmfDhg20bt0aR0dH6tevz7x588o85zWUSmbx4sWKg4ODMnfuXOXQoUPKmDFjFC8vLyU5OVlRFEUxGo0KoBiNRkVRFGXr1q2KwWBQPvroI+Xw4cPKG2+8odjb2ysHDhzQ8o9R6f3b9+lqw4YNU2bMmKFERUUpR44cUZ544gnF09NTOXfuXDknr1pK+n26LCYmRgkKClK6dOmi3H///eUTtooq6fcoLy9PadOmjXLvvfcqW7ZsUWJiYpQNGzYo0dHR5Zy8ainp92nhwoWKo6OjsnDhQiUmJkb5888/lYCAAOWll14q5+RVx/+3d3chTf1xGMAf06YGSoT4FhZMiMIS0VCmoRaCkNRVKBZDorDQroRKlFhkmoR0Myp7tyulQiFShmUFRXrjC0S+hA3rxglSlGSwt+//ohx/37Ktdo7H83xgF/78HXnGl+HD2c5ZV1eX1NbWSnt7uwCQjo6O3+632+2yYcMGqaqqkuHhYbFarRIaGio2m02ZwL+suSKXmZkplZWVvp89Ho8kJibKpUuXRGRxkSsuLpaioqJ5fyMrK0tOnDihXGgdWmlOK3G73RIVFSX3798PVkSSwObkdrslOztbbt++LWVlZSxyQebvjK5fvy5Go1GcTqdSEUn8n1NlZaXs27dv3lpVVZXk5OQENSf99CdF7syZM5KSkjJvraSkRAoLC4OYbLE19daq0+lEf38/CgoKfGvr1q1DQUEBent7lzymt7d33n4AKCwsXHY//b1A5rTQ7OwsXC4XNm3aFKyYuhfonC5cuIDY2FgcO3ZMiZi6FsiMHj9+DJPJhMrKSsTFxWHnzp1oaGiAx+NRKrbuBDKn7Oxs9Pf3+95+tdvt6Orqwv79+xXJTCtbLf1B9W92+Jemp6fh8Xh83woxJy4uDqOjo0se43A4ltzvcDiCllPvApnTQmfPnkViYuKiFxH9O4HM6fXr17hz5w6GhoYUSEiBzMhut+P58+c4cuQIurq6MD4+joqKCrhcLlgsFiVi604gczp8+DCmp6exZ88eiAjcbjdOnjyJmpoaJSLTH1iuP3z79g0/fvxAZGSkIjnW1Bk50ofGxka0tbWho6MDERERasehX2ZmZmA2m3Hr1i3ExMSoHYeW4fV6ERsbi5s3byIjIwMlJSWora1Fc3Oz2tHof16+fImGhgZcu3YNAwMDaG9vR2dnJ+rq6tSORqvMmjojFxMTg9DQUExNTc1bn5qaQnx8/JLHxMfH+7Wf/l4gc5rT1NSExsZGPHv2DKmpqcGMqXv+zunDhw+YmJjAgQMHfGterxcAEBYWhrGxMSQnJwc3tM4E8lpKSEjA+vXrERoa6lvbsWMHHA4HnE4nDAZDUDPrUSBzOnfuHMxmM44fPw4A2LVrF75//47y8nLU1tbO+w5yUsdy/SE6Olqxs3HAGjsjZzAYkJGRgZ6eHt+a1+tFT08PTCbTkseYTKZ5+wHg6dOny+6nvxfInADg8uXLqKurg81mw+7du5WIqmv+zmn79u14+/YthoaGfI+DBw9i7969GBoaQlJSkpLxdSGQ11JOTg7Gx8d9JRsA3r9/j4SEBJa4IAlkTrOzs4vK2lz5Fn19RfqqtWr6g6KXViigra1NwsPDpaWlRYaHh6W8vFw2btwoDodDRH5eUYIFtx8JCwuTpqYmGRkZEYvFwtuPKGClOZnNZqmurvbtb2xsFIPBII8ePZLJyUnfY2ZmRq2noAv+zmkhXrUafP7O6NOnTxIVFSWnTp2SsbExefLkicTGxsrFixfVegq64O+cLBaLREVFSWtrq9jtdunu7pbk5GQpLi5W6ymseTMzMzI4OCiDg4MCQK5cuSKDg4Py8eNHERGprq4Ws9ns2z93+5HTp0/LyMiIXL16lbcf+VesVqts2bJFDAaDZGZmSl9fn+93ubm5UlpaKl6v17f24MED2bZtmxgMBklJSZHOzk41YuvO7+aUl5cnZWVlvp+3bt0qABY9LBaL8sF1xp85LcQipwx/Z/TmzRvJysqS8PBwMRqNUl9fL263W+HU+uPPnFwul5w/f16Sk5MlIiJCkpKSpKKiQr58+aJ8cJ148eLFkv9n5uZSVlYmeXl5i45JS0sTg8EgRqNR7t27p3juEBGeoyUiIiLSojX1GTkiIiIiPWGRIyIiItIoFjkiIiIijWKRIyIiItIoFjkiIiIijWKRIyIiItIoFjkiIiIijWKRIyIiItIoFjkiIiIijWKRIyIiItIoFjkiIiIijWKRIyLda21tRWRkJCYnJ31rR48eRWpqKr5+/apiMiKi3wsREVE7BBGRmkQEaWlpyM3NhdVqhcViwd27d9HX14fNmzerHY+IaFlhagcgIlJbSEgI6uvrcejQIcTHx8NqteLVq1cscUS06vGMHBHRL+np6Xj37h26u7uRl5endhwiohXxM3JERABsNhtGR0fh8XgQFxendhwioj/CM3JEpHsDAwPIz8/HjRs30NLSgujoaDx8+FDtWEREK+Jn5IhI1yYmJlBUVISamhqUlpbCaDTCZDJhYGAA6enpascjIvotnpEjIt36/PkzsrOzkZ+fj+bmZt96UVERPB4PbDabiumIiFbGIkdERESkUbzYgYiIiEijWOSIiIiINIpFjoiIiEijWOSIiIiINIpFjoiIiEijWOSIiIiINIpFjoiIiEijWOSIiIiINIpFjoiIiEijWOSIiIiINIpFjoiIiEij/gNGVovlESQJUQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x26bc4e3bb10>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "y_1=y.subs([(c0,sol_1 [0][0]), (c1,sol_1 [0][1])])# 基态试探解\n",
    "y_ex_1= sqrt(2) *sin(pi* x) # 基态精确解\n",
    "plot(y_1,y_ex_1,(x,0,1),ylabel='y(x)', legend=True)\n",
    "\n",
    "#fig1.save('fig1.png',dpi=100)\n",
    "#plot.savefig('xxx.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "21b0d17d-aef0-4327-b326-c47f59d3bc22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x26bd3fde350>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_2=y.subs([(c0,sol_2 [0][0]),(c1,sol_2 [0][1])])# 基近似探解\n",
    "y_ex_2= sqrt(2) *sin(2*pi* x) # 基态精确解\n",
    "plot(y_2,y_ex_2,(x,0,1),ylabel='y(x)', legend=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "13120c2f-2c4c-4c9f-a458-092f4e64d535",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NIpEI69atg0QiwerVqxEbGwuj0YjmzZsLHc2n+W0fpVQqRWhoKF577TW6BrACRUVF6NevHwYPHozt27dj9uzZGD16tNCxSA0lJSUhNTUVffr0gdlsxueffy50JJ/mty1KmgqianJzc9GsWTOIRCI0bdqU/qn4iQkTJiAlJQWPPfYYpk6dCsYYXQtbAx4plEajERMnTkRWVlaFy5nNZuj1enAcB7PZDKVSyZ9QqOg5Uj2XL19G586dsWzZMkRGRuLw4cP0YfITderUQVJSEl544QWMGDECQ4cOhUajQUREhNDRfBNzM51Ox7KyslhVNiWRSPjvTSYTUygUVXquPEOGDKlG2trj9u3bLCIign377bds+PDhTKPRCB2JuME777zDXn/9dfbZZ58xqVTKCgsLhY7kk9x+1luhUEAikVS6nNlstvuZ4zgYDIZKnyPVs3DhQkilUty8eROnT5/G7NmzhY5E3CA+Ph4//fQTQkND0bp1a3z00UdCR/JJXtNHaTAYEBwcbPdYcHAwjEYjjh496vC5qhRhYu/s2bNIT0/HDz/8gN69eyMlJQV169YVOhZxg4cffhgbNmzAlClTYDAY8NdffwkdySd5zXWUVqu13Mfz8/MrfI44hzGGdu3aITs7Gxs2bEDfvn3Rq1cvoWMRN+rfvz+6d++OrVu3onv37njnnXdw9+5doWP5FK9pUTriqEhW9pxtUAwbukzogXnz5kEmk0EqleKTTz5BTk6O0JGIByxfvhxSqRSvv/46Tp06hcWLF+Of//yn0LF8htcUSrFYXKaFmJ+fD7FYXOFzjtDlQWUdPHgQOp0O77zzDmJiYvDuu++iadOmQsciHtCqVSvMmTMHs2fPxqZNm9CtWze88sor6NGjh9DRfILXHHrL5fJyH5fJZBU+R6rmzp07iI2NxaZNm/Ddd9/h6tWriIuLEzoW8aDZs2fj119/hdFoxPr163HhwgWhI/kMj7YorVarXSvQaDRCLBaD4zhwHGe3rNlshkwm41uUjp4jVRMUFIS1a9eid+/eiIiIQEpKCs0JXcsEBQVhzZo1mD59OnJychAQEIBjx45Rq7IK3N6iNBgMUKvVAB5MearX6/nnSv+s0+mgVquh1+uh1Wqh0+mq9Byp2C+//ILt27cjKioKy5YtQ+/evekETi0VFRWF8PBwrFu3DleuXMFLL72E06dPCx3L6/ntvd40HuUDRUVFePbZZzFlyhS8+OKLkEqlOHbsGEJDQ4WORgRiMpnQq1cv5OTkQK/XIz09HQaDge7KqoDX9FG6Gk0F8cDGjRvRsGFDjBkzBiqVCrNmzaIiWcuFhYUhNjYWb7/9NiZNmoS7d+/i0KFDQsfyatSi9HPz589HXFwcrly5gtdffx2//vor6tWrJ3QsIrCbN28iPDwc//nPfxAREYGgoCAaOKMCftuiJA/uwFm6dCk4jsPs2bOh0WioSBIAwCOPPIJ//vOfmDNnDurWrYt//etfmDJlitCxvBYVSj9lMBgwcOBAFBcX44svvkBQUBAUCoXQsYgXGTt2LKxWK7766iv0798fe/bsoUNwB6hQ+qG7d+9i2rRpWLNmDe7cuYMFCxZgxYoVdFhF7NSpUwcrVqzAvHnzEBQUhJUrV2LSpEm4f/++0NG8jtfcmUNc5/PPP0fXrl0RFRWFxYsX4/nnn0dkZKTQsYgX6tOnD7p06YKNGzdixowZCAgIoH+o5aCTOX6oqKgIN27cwN27d9G1a1dkZWXRHM/EoVOnTuH555/HyZMnIRaLsW3bNgwYMIBuby3Bbw+9a+vlQTNnzsQvv/wCsViM999/H7GxsVQkSYU6duwIhUKBhIQEAA9uUHj77bcFTuVdqEXpR/bv34/x48fjl19+wdmzZ/Hiiy8iNzcXjRs3Fjoa8XJXr17FE088gSNHjiAkJASdO3fGjh07aDyF/89vW5S1TVFREWbOnIkVK1agXr16iI+PR3x8PBVJUiVNmzbFzJkzsXDhQjzyyCNITEzEd999J3Qsr0Enc/zE7du3MXr0aAwZMgQHDx5ETk4Otm/fLnQs4kNmzZqF8PBwHDt2jB+79e+//0b9+vUFTiY8alH6gevXr+PMmTOYP38+AECtVmPx4sUICgoSOBnxJfXr18e7776L+Ph4AMD58+fx5JNP4vbt2wInEx4VSj/w0UcfYePGjQCA//znP7h9+zZGjhwpcCrii8aNG4dz585h3759aNOmDXr27Inly5cLHUtwfnsyRyqVIjQ01O+ngDh79iyefvpp/PLLLwgODka3bt2wcuVKREVFCR2N+KgdO3YgISEBhw8fxsWLFyGRSHD8+HG0aNFC6GiC8dsWpW0qCH8ukgCwfv16zJ07F02bNsXWrVvRokULKpKkRoYPH46AgACkp6ejVatW+Prrr2v9NZV+26KsLZcH3b9/H8XFxWCMITw8HDqdji7pIDX2/fffY9KkScjJyUFgYCD0ej06d+6MLl26CB1NEH7bovR3jDGMGjUK58+fR1BQEJKTkyGVSqlIEpd44YUX0KZNG2zbtg0AkJeXx58srI2oUPqonTt34tSpU2jXrh1u3bqFhIQEfPDBB0LHIn7ko48+wvvvv4+7d+8iNjYWZ8+ehcFgEDqWIKhQ+qD79+8jPj4eS5cuRZ06dbBmzRpERUUhIiJC6GjEj0ilUkilUiQlJSEwMBCJiYn46aefhI4lCOqj9EHXr19HcnIy5s6dC6vVik6dOuHw4cNo166d0NGInzl58iTkcjl+//13NGjQAMCDYfweeughgZN5lt+2KP11UIzbt2/jwoULmDt3LgBgxYoVUCgUVCSJW3Tu3Bn9+vXD+vXrATyYKrp79+64d++ewMk8q8IW5dmzZ6HT6ZCRkQGLxcI/HhwcjKioqCp/QM1mM/R6PTiOg9lshlKpdDgnt16vh1wuB4AyyxiNRgCARCKB2WyG1WqFRCIpdz3+2qJcunQpfv75Z6SkpODatWuIiIigWRWJW50+fRq9e/fG77//jkaNGmHo0KEYOHAgJk+eLHQ0z2EOqNVq9tZbbzGj0Vju80ajkV+mMhKJhP/eZDIxhULhcFkAZb40Gg1jjDGlUsk/JpfLmcVicbieIUOGVJrL11gsFta8eXN2+vRpxhhjKpWKzZ49W+BUpDaYMGEC++CDDxhjjOXk5LCWLVuyW7duCZzKc8otlImJicxqtVZpBVartcJiaTKZ7AolY4yJxeJyl7VYLEyn09k9ZiuSjDGm1WqZxWKpsEDa+GOhXLp0KZs8eTJjjLFLly6xpk2bsr/++kvgVKQ2OHv2LGvWrBnLz89njDFmMBhYYWGhwKk8p9w+yvnz51d5eK7GjRvzA36Wx2AwIDg42O6x4OBg/jC6tJITYOn1+jITYonFYoeH7f5u1qxZ0Gg0AIAlS5Zg/PjxaNasmcCpSG3Qtm1bKBQKrFixAgDQr18/pKeno6CgQOBknlGlkznXr1/H2bNnq7UBq9Va7uP5+fllHitZAK1WK/Lz88FxnN1jer0eer0earUaZrO5Wpl8UWJiIo4ePYqGDRvi0qVLSE1Nxbx584SORWqR+Ph4aLVa/rO7b98+rFy5UuBUHlKVZqdarWYdOnRgjD041E5OTq5yk1Wj0TC5XG73GMdxZQ6xS1MqlWUOsUv+nJWVxTiOc/j7EomEDRkyhP9KTU2tcmZv88cff7CmTZuyK1euMMYYmzFjBouPjxc4FamNpk2bxt5++23GGGMXLlxgzZo1Y9euXRM4lftVqVDq9foyj1W1WGq12nL7KDMyMhz+jsViKbcIZmVl2S0DgJlMpnLX4U99lJMnT2YLFy5kjP1f0awNb07ifS5evGj3/ps7dy7bunWrwKncr0qH3hKJBJGRkVi2bBl/CM6qeJ267VKf0iq6J/no0aPlXhrUr1+/MsuW7v/0N4wxBAQEYM6cOQAAjUaDiRMnIiQkROBkpDZq2bIlXnvtNb6vcunSpXj99dcFTuV+VSqUSUlJWLJkCRhjUCgUCAkJQVhYWJU2ULKPEXhwTaVMJuMLodFoLNPXaDQayxRAjuP4ExnAg5NECoXC70/s5OXlYe3atWjSpAn+/PNPfPnll3zRJEQIb731FpKTk5GXlweRSAS9Xo8FCxYIHcutqlQoOY5Dv379MH/+fBw9ehQGg8HhSZry6HQ6qNVq6PV6aLVa6HQ6/rmEhATo9fpyt1mSWCyGTCZDYmIikpKSkJmZabcef3Tu3Dl069YNd+/eBfDghM6ECROoNUkE1aJFC4waNQqrVq0CADz//PNITk7G5cuXhQ3mRlW61/vMmTP49ttvMXLkSDRq1Ajx8fEICwvDhAkTPJGxWvzhzhylUonWrVvjnXfeweXLl9G1a1ecPHkSjz76qNDRSC138eJF9OjRA7/99huaNGkClUqF+/fv84fk/qZKLcr27dtjwoQJaNSoEYAHrb3SLT7iWufOncPOnTsxY8YMAA/6gsaPH09FkniF0NBQREdHY/Xq1QAeXHvduXNngVO5T5kWZUFBASwWi1ODLFy/fh0A+ELqDXx9zpx79+7hxIkT6N69O65cuYIuXbrgxIkTdIE58Rrnz59HZGQkfv/9dzRu3BhFRUU4ceIEnnzySaGjuVyZFmXjxo2RkZGBf/3rX1VaQXp6OtLS0ryqSAK+PWfOH3/8gfT0dHTv3h0AsHz5cowZM4aKJPEqbdq0wfDhw7F27VoAwLVr19CvXz9cvXpV4GSu57CP8tixY0hISEBYWBgiIyPBcRzEYjGsVivMZjOOHDmCM2fOIC4uDn379vV07kr5ch/ljBkz0KhRIyxevBh5eXkIDw9HdnZ2rZ4Fj3inM2fOoGfPnjh9+jQeeeQRzJo1C/Xr18dHH30kdDSXqvRkTkFBAdLS0mAymWC1WiEWixEWFga5XI727dt7KqfTfLVQlj5ps2jRIuTl5WHdunVCRyOkXOPGjcMTTzyBefPm8dPbms1mfqBff0AjnHuZbdu24cSJE0hISEBBQQE6duyIo0ePok2bNkJHI6Rcv/32G/r27YvTp0/j4YcfxqVLl/zu6KdKZ73feustxMfH47vvvnN3nlrv9ddf5w9bNmzYgKFDh1KRJF6tU6dOeO655/DJJ58AAB577DG89dZbuHHjhsDJXKdKhTI+Ph4cx2HTpk0IDg7GgAED7G5n9Ea+OBXEhx9+iK1bt0IkEuHWrVtYs2YN3nrrLaFjEVKpBQsWIDExEYWFhRCJRLh8+TKSkpKEjuUy1Tr0NhqN/Ac4LCwMGzdudHmwmvK1Q+8bN26gQ4cOOHLkCNq2bYvVq1fj8OHDSE1NFToaIVUydOhQDB8+HOPHj8fJkycRFRWF06dPo169ekJHq7Eqj0dZ8rBbIpEgLi4Oe/fuhVKpxLJly9wWsLbQarUYOHAg2rZti8LCQixfvhzx8fFCxyKkyhYsWIAlS5agqKgInTt3xrBhw/Dbb78JHcslAquykEqlQn5+PuLi4iCXyyGVSpGVlYVXX30VPXr0qFUD6LpLixYtMHjwYADA1q1b0aNHD3Tt2lXgVIRU3TPPPINWrVohPT0dI0eOxPr168EYQ3FxMerU8e0JX6uUXiqVIi0tDadOnYJcLofFYoFKpUJBQQFkMhlEIpG7c/q1s2fPIiYmBuHh4SgqKsKSJUuoNUl80oIFC/DRRx/xwzBOmjTJPwavqerAlenp6eU+7miWRqH5ysC9RUVF7PHHH2eHDh1ijDH25Zdfsr59+wqcipDqKS4uZpGRkWz37t2MMcb27t3LevTowYqLiwVOVjNVbg+/8sor5T7eo0cPlxXt2mjnzp1o3rw5nn76aTDGsGTJEjrTTXyWSCRCfHw8lixZAuD/Bu42GAxCxqox3+44qICvXB60dOlSqNVqAMDevXsREBDgcFR4QnzBsGHDcPXqVRw8eBAikQirV6/GY489JnSsGqE7cwR28uRJhIeHQyQSoU+fPpg2bVqZKXoJ8TVbtmxBeno6vvrqKwDAn3/+icLCQqdGJfMmftui9AUbN25EixYtIBKJ8NNPP+HSpUsYMWKE0LEIqbHRo0cjOzsbOTk5AIAdO3b49HQRVCgFkpubiw8//BD169cH8GDSMJVKhYCAAIGTEVJzQUFBmDNnDj/P1bhx4/Dtt9/i3LlzAierHiqUAlmxYgWmTZuGoKAg/Prrrzh69GitmM2O1B4TJkyAwWDA2bNn0aBBA0ycOBEbNmwQOla1UB+lAO7du4fIyEjs27cPTZo0wfjx49G5c2fMnz9f6GiEuNSiRYtgtVqxevVqFBQUIDAw0CeHX/PbQuntU0EwxiASifDHH39AIpHg1KlTaNy4sdCxCHGpq1evIiIiArm5uQgJCUFmZiZMJhNGjRoldDSn+O2ht7dOBXH79m3069cPhYWFAIDVq1dj/PjxVCSJX2ratCliYmKwfv16AED9+vUxf/583Lt3T+BkzqnSvd41ZTabodfrwXEczGYzlEolxGJxucsajUYA4EdJtlqtkEgkTq/HW6WkpEAsFuOhhx6C1WrFli1bkJ2dLXQsQtxmzpw56NWrF+bNm4cuXbogIiIC6enpvtWq9MTtPxKJhP/eZDIxhULhcFmlUskAMABMLpczi8VSrfV44y2MxcXFrEuXLuzAgQOMMcYSEhJYbGyswKkIcb9Ro0axdevWMcYY++abb9icOXMETuQct7coS48sxHFchbczSaVSWCwWALBrLTq7Hm9048YNDB48GM8++yzu3r2LtWvX4ttvvxU6FiFuN3/+fERHR2PSpEkYMGAABgwYIHQkp7i9j9JgMCA4ONjuseDgYP4QuzxisbjMIXV11uNt7t+/jyVLlkAkEiElJQUymQzh4eFCxyLE7SQSCdq1a8dPg/3DDz/gzTffFDhV1bm9UFqt1nIfz8/Pd7i8Xq+HXq+HWq3mW5LOrsfb5ObmIjIyEsXFxSguLsayZcvociBSq8yfPx9Lly4FYwwSiQRff/21z1yALthZb0eFT6lUQqFQQKFQICYmBlFRUdVaj21QDNuX0INjrFmzBrGxsahTpw6+/vprNG7cGM8++6ygmQjxpAEDBuDOnTv4/vvvUb9+fcTGxvrMBehu76MUi8VlWn35+fkOz1abzWb+LLft7LbZbHZ6PbbLg7yB1WpFWloacnNzAQDLli2DSqWiAY9JrSISifhWZZ8+fTBlyhT8+9//FjpWlbi9ReloyDCZTFbmMaPRiH79+pV5PDg42Kn1eJuHHnoIaWlpePTRR5GZmcm3dgmpbUaNGoWcnBz8+uuvaNWqFaZOnYrLly8LHatSbi+UHMfZ/Ww2myGTyfiWoNFo5PshOY7jb6IHHpzAUSgUEIvFla7HWxUVFWHv3r148cUXAQDLly/HnDlzaPALUivVrVsX06dPx4oVKwAAhw8fRv/+/fmpI7yVR25hNJvN0Gq1iIyMRGZmJuLj4/kCFx0djcjISKhUKgAPCqfBYIBYLIbJZLIrnBWtpzRvudf7q6++wtKlS7F//36cPXsWzzzzDMxmMz9qECG1TUFBATp06ICcnBw0b94cEokEK1euRJ8+fYSO5pDf3uvtLYUyKioKSqUS0dHRmDVrFho1aoQPPvhA6FiECGrOnDmoX78+Fi9ejE8//RS7du3Cjh07hI7lkN8WSm8YFOP8+fPo3bs3TCYTbt68iccffxy//PILmjdvLkgeQrzFuXPn8NRTT8FsNiMgIAA///wznnnmGaFjOUSDYrhRmzZtkJOTg7p16yIpKQnDhw+nIkkIgLZt26Jv377YsmUL6tWrh7CwMGRkZAgdyyG/LZRCu3nzJlQqFRo1aoTCwkKsW7cOc+bMEToWIV5j7ty5WLVqFYqKinDz5k2MGTMGd+/eFTpWuahQusm2bdtw4cIFiEQipKWl4cknn0Tnzp2FjkWI15DJZGjZsiW++uortG/fHpGRkdDpdELHKhcVSjdgjGH9+vWYOnUqGGNYvnw55s6dK3QsQrzOnDlzsHz5cgDA1KlTsXXrVoETlY8KpRv8+eefaNOmDZ599ln873//A2OMv46SEPJ/hgwZgr/++gtHjhxB//79vfbMNxVKNwgNDcXu3bshEon41iTdrkhIWXXq1MGsWbOwYsUK1KlTB+fOneMvRvcmdHmQi125cgUxMTH47rvv8Pvvv6Nfv34wm80ICgryWAZCfMmtW7fAcRwyMzPRoEEDdOrUCSaTyaumR/HbFqVQlwdt3rwZEREREIlEWLVqFaZMmUJFkpAKNGjQALGxsVi7di1CQkIwaNAgr+ur9NsWpRB35hQXF6NDhw7YuXMnWrZsifDwcH72OUKIYxcvXkT37t1hNptx4sQJbNu2DevWrRM6Fs9vW5RCKCgowJgxY9C1a1dotVooFAoqkoRUQWhoKF566SV8+umneOaZZ7yqSAJUKF1KJBLh/fffR2FhITZs2IBZs2YJHYkQnzF79mysXr0aRUVF+N///oeJEycKHYlHhdJF/vjjD3Tp0gX379/H9u3b0a1bN3Tq1EnoWIT4DIlEgtatW2PXrl2QSqXYsWMHrl27JnQsAH5cKG2D43pqCojNmzcjJiYGAQEBWLlyJd2uSEg1zJ49G6tWrULDhg3xyiuv4PPPPxc6EgA6meMSRUVF4DgO33zzDa5evYpp06bh+PHjdO0kIU4qKirC448/Dp1Oh4CAABiNRq+YrdFvW5SeVFRUhFWrVqFz585YuXIlZs2aRUWSkGoICAjAjBkzsGrVKnTr1g1jx47F9evXhY5FhdIVjhw5gsGDB8NsNuPQoUMYPXq00JEI8Vnjx4/Hnj17cOnSJWzduhVTpkwROhIVypq6ePEiXnnlFRQVFWHNmjVQKpWoV6+e0LEI8VkNGzbEmDFjsGHDBowYMQJ79uxBXl6eoJmoUNbQp59+itGjR6OwsBApKSmYPHmy0JEI8XkzZsxAcnIy6tatixEjRgh+Usft83r7M8YYNm/ejF27dmHz5s14+eWX8dhjjwkdixCf165dOzz77LNITU2FSqXCrVu3BM3jt2e9PTUoxtmzZ9G6dWv+TJ1EInHbtgipTQ4cOICpU6fi+PHjuHDhAoqLi9GuXTtBsnikRWk2m6HX68FxHMxmM5RKpcNpZm3T1QJAZmYmkpOT7eYABx5cmGo2m2G1Wh0WJtugGO706aefYtCgQfjPf/6DVq1aUZEkxIV69+6NwMBA7Nu3D9nZ2Thx4gSSk5OFCcM8QCKR8N+bTCamUCgcLqvRaOy+L/m7SqWSAWAAmFwuZxaLxeF6hgwZUrPQlbh27RoLCQlh169fZ3369GHp6elu3R4htdFnn33GhgwZwq5evcp/3oTg9pM5ZrPZ7meO4/gWY2lGoxEJCQn8zwqFAkajkV+HVCqFxWKBxWJBRkaGw1apJ2zbtg3Dhw+H2WzG2bNnMWzYMMGyeAuj0Qi1Wi10jApJpVLo9XqhY9SYwWCAVCpFUlJSjdbj7a9HTEwMjh49CqvVCrlcjrS0NEFyuL1QGgwGBAcH2z0WHBzMH0aXJJFI7JrWVquVX95GLBYLWiBt9uzZg9jYWKxevRrTpk1DQECA0JEEp9Vqa/zBdTeNRgO5XO629dves+4ml8sRExPj9O+Vzufu16OmHnroIcTFxWHt2rVYuXKlYNNPu71QOnrj5Ofnl/u4QqHgv9++fTvkcjlfGK1WK/R6PfR6PdRqdZnWqift3r0bYWFh2LVrF2JjYwXL4U3EYjGsVqvDIwZvUPL95Gpms1mwFk9VlJfPna+Hq0yaNAmpqalo0KABDAYDTCaTxzMIdnlQZf95bUUxKyuLf6zkSSCO4xAVFeXwRbMNimHjyrPfiYmJ6Nu3L7755hvExMR4/RvNEwwGA2JiYmA0GqHT6by6leIuGo0GUqlU6BgOeXs+R5o3b46XX34Zn376KfLy8nDw4EFoNBrPhnB3J6hWq7U7IcMYY2KxmGVkZFT4e0qlkplMJrvHsrKy+O8tFgsDUGYZG3edzPn777/Zo48+ys6dO8dCQ0NZbm6uW7bja2wn4XQ6HROLxXbPZWRkMI7jmFKpZDqdjmm1WqZUKvmTcVV9XqvV2r2fsrKymEajYTqdjmk0GmYymZhOp2MSiYRxHMfn4jiOaTQalpWVxSQSCdNqtfx6bT9nZGQwrVbLFAoFM5lM/LqVSqXdvuh0On5ZlUplt48SiYQpFAqm1Wr592VGRgafseTypVksFj5HyWXL28eSr3npfSn5d+A4jv+clZev9OtR0fYcvVaekpWVxcLCwtjvv//OWrRowQoLCz22bcYYc3uhNJlM5RbKis5Yl/wDWSwWZrFYWFZWlt0H0FYoHa3HXYUyNTWVDRkyhKWkpLCBAwe6ZRu+qOTVCgDK/CNUqVR2y+h0OiaXy6v8vFKp5IuWTqdjJpPJ7nnGHlxdYXu/2L7XarV275GSxcW23ZIfeLlcbpeD4zi73y/5z9lW2Euuq+S6S7/3tVqt3bpL0mg0dq+ZrZg52sfy9kWj0ditX6FQ2K2zdL7S66hse+W9ViUbL+723HPPsV27drG+ffuygwcPemy7jHngrDfHcXY/m81myGQyu2sjS/Y16vV6SCQScBwHq9WKtLQ0iMVicBxn19w2GAxQKBQeP+w9f/48lEol1qxZg5kzZ7p9e4sXL0a9evX4r0uXLmH79u12j+3fvx/Hjh2ze+zjjz/GrVu37B5TqVQAgLCwMP6x4cOHAwAGDhyIevXqYfHixU5ntPUbJSUlISkpCRzHQafTlVmu5N9KoVDAYDDYdcFU9LxYLEZYWBj/nFarLXPdKsdx/PslOTkZUqnU7r1WnpCQEERGRtplKPmeFYvFdv3pFouFvx44Pz+/wn5yrVaL4OBgGAwGu2uDy6NQKBAdHQ2pVIrExESMHDmywn10h8q2V95r5ehcgzvMnDkTq1atwjfffINevXp5bLuAh/oodTod1Go1IiMjkZmZafchSkhIQGRkJFQqFcxmM6Kjo+1+VywW832TMpkMiYmJEIvFMJlM5X4Y3U2tVuPw4cMoKChA//793b69hQsXYuHChXaPxcTElHvG886dO1V6rLx+3T179lQ7o9FohFar5X8ODg7GxIkT7R5zhdL/dCsiFoshkUiwfft2p28EqKiwJiQkICQkBAqFosI8tgIvkUjs+muVSmW5ywcHB8NiscBoNGL79u2Ijo526w0MVqvV5/rWhw0bhrlz5+K3337Dp59+CrVajWbNmnlk2x4ZFMPWGlQoFNBoNHZ/IJ1Ox7d0OI4De9AdwH9ZLBZ+WYlEApVKBaVS6fnOXABLlizBJ598gjVr1mD69Ok05qQDCoWi3LPfJVuPer2+zBnXyp4v2XqJiYkps36j0YiRI0fy29bpdPxdYY5ylMfR8waDAUajESqVij/isT1e3rLlZXR0RUBCQgLMZjMkEgn/GaloH8vLKhaL7UbZKd1id5TDtkxVtiekwMBATJkyBWvXrsWNGzeQkpLiuY179EDfg1zdR1lcXMw6dOjAMjIyWNOmTdmNGzdcun5flJGRweRyOZNIJHZ9VVqtlonFYrsTBSqViimVSruTFSX7/ip63nYiQS6X2/W5lT5RkpWVxbRaLX/yhrEHfXBisdjuZI5cLrc7mWHLbzsBYjuhY9sP24kli8XC9/vZvhQKBd9PaTKZmFKpLHMyR6VSMZ1Ox3Q6ncM+dVtfoe1klm2d5e0jY6xMdsYe9NvbXkNbNtu+lpev9OvhzPZKv1aekpeXx0JCQtiePXtYt27dPLZdGhSjig4ePIjp06dj8ODBuHXrFpYvX+6ClLWHWq1GWFiYw0PPyp4nxCYuLg4cx+F///sftm3b5pEpof12mDVXD4px//59zJs3D3PnzsXBgwddtl5CiHOmT5+OQYMGwWQyITDQMyWMBu6tgnv37qFnz564d+8ennrqKadOKhDwZ311Ol25t65W9jwhJT3xxBPo0KED0tLS0Lt3b9y7d8/t2/TbQ29XzsKYmpqK3bt34+TJk1i2bBn69u3rkvUSQqpn165dWL58OQIDAzFz5ky7u/DcgVqUVfDZZ5/hiSeeQGFhIV588UWh4xBS6w0aNAgXLlzAiy++iC1btrh9e37bR+kqFy9exLFjx9CoUSPMmDGDLgkixAsEBARg2rRpOH78OFq1agXGmFs/m3576O2qs96XL1/G7t27ER8fjzNnzqBBgwYuTEkIqS6r1YoOHTogNzcXjRo1QlBQkNu25bctSled9bZYLDCbzRg3bhwVSUK8iFgsxsiRI/Hee+/h+PHjOHDggNu25beF0hWOHz+OV199FTdv3sShQ4eEjkMIKWX69OkYMGAAiouLcfr0aXTo0MEt26GTORX4/PPP0bVrV/Tq1Uuw2d+8mdFoRFxcHEQiEdRqNZKSkpCYmAi1Wo0mTZp49QC+5akt0yv4k86dOyM8PBwymQxbt25134Y8dg+Qh9X0FsZ79+6xxx57jEVERLB9+/a5JpQfMplM5Q53Z7ud0F0qGqavJkoPXVadLBkZGW7LR8ratWsXk8lkbOfOnW7bBrUoHRCJRFi0aBECAgLwwgsvCB3Ha5WeD8nGnSPfeNOUC746vYI/efnll5Gfn49HH30UV69edcs2qFA6YDAYsHfvXholyEklxxd116gzQowc5Yg3ZamtbJcKzZ49G++++65btuG3hdI2Z84XX3zh9O/eunULo0aNwg8//IB//OMfbkjnf2z9kxMnTuQfE4vF0Ov1kEql/KC7iYmJCAsLQ2JiIoAHw6kZDAYkJSWVmerWbDZDrVZDr9cjKSmJHz7t6NGjyMjIQFJSUoUD51qtViQlJcFgMPAT0gEPinliYiL0ej0SExMdrsPWZ1kya1hYGN/3Wl4Wo9FYpp/T0fZK9onaXoPS47GSqnnzzTdx6tQppKWlobCw0PUbcNtBvcBq0keZkpLCHn/8cTZ//nwXJvJPpafkKD2vi20ZR1MzwMHUChaLxW4ahpJTRZQ3pUF5aHqF2mXy5MksLCzMLX2VdHlQObZt24YrV65g6tSpQkdBgwYNUFRU5LHtBQQE4NatW9X+/ZLTDRsMBr6/zjY1g06ns+u/s1gsEIvFZaZWSEtLA8dx/LLx8fHVyiKVSsFxHGJiYqBUKpGQkOBwugN3DPFW0fQKSqUSISEhdsOEeXp6BX8ybdo07NixA08++aTL102FshyDBg1C3bp10bZtW6Gj1KhoCaHkyEolD2kdTc3gaGqF0lMVODo5UtGUBjS9Qu0SERGBJ554Al988QWmTp2KRo0auWzdfttHWV179uzB2rVrMWvWLKGj+ARHrR+r1crPye5oaoaKplZQKBRlhlxzNOWCIzS9Qu0zffp0rFixAunp6S5dL7UoS5k3bx4KCwvRp08foaN4vZKTiiUkJPAnbGwzMsbHxyMpKQkajQZxcXEAgMjISEycOBFms5mfNM5WSKKjo6HVasFxHDiOg1ar5SelA8BP0hUXFweNRoOkpCS7ibtKCwkJgcFgQHBwMPLz8xETE8MXzcTERHAcx092JxaL+ZanbVsSiQQjR46EWq3mM8rlcv5wmuO4Mlls6wgODoZCoXBqe7aTQSVfA+KcQYMGISAgAJs2bcKbb77psvXSoBglmEwmdO3aFcuXL8fkyZPdnJAQ4g4ajQaLFi3CmTNn0KJFC5es028PvW2DYjgzcpDtkPCNN95wVyxCiJsplUrUr1/fpdNEeOTQ29YvZZs43nbI5eyyzqynOm7cuIFJkybRKEGE+LAmTZrg1VdfxZQpU6DT6VyzUpdfcFQOiUTCf28ymeyuG3NmWWfW4+x1lFlZWaxhw4bMbDY79XuEEO/z888/s4CAAJabm+uS9bn90Lv0XQ8cxzk8U1nRss6spzreffddtGzZEu3bt3fZOgkhwujWrRtCQ0Px3nvvuWR9bi+UtrOOJQUHBzucjc/Rss6sx1lFRUXIyMjAW2+9VeN1EUK8w4wZM7B7926XrMvthdLRNWflXX9X0bLOrMdZO3fuRFBQEMaOHVvjdRFCvMPMmTMRHByMnJycGq9LsOsoHRU+Z5d19JxtUAybii4T6tOnD/bv30+jBBHiRwIDA6HX69GmTZuar8sFeSpU3r2r+fn55Z6trmhZZ9YDODdnTnBwsMNxFQkhvksmk7lkPW4/9HZ050R5O1DRss6shxBCXMntLcrSt2GZzWbIZDK+JWg0GiEWi8u9ZavksqVbjqXXQwgh7uKRPkqdTsffs2u719UmISEBkZGRUKlUlS5b0XOEEOI2Lrka0ws5e8F5amqqm5J4lj/sB+2Dd/CHfWDMNfvht/d6OzsVRHWmjPBG/rAftA/ewR/2AXDNfvhtoazOoBjOcvYP4O7lq4P2wX2/4+7118a/hVDF228LpSf4w5uC9sF9v+Pu9dfGv4VQhdJvx6Ps0qULP5BsVVy8eBGhoaFObcPZ33H38t6YyR/2gTLVrkyhoaHYuHGj3WN+WygJIcRV6NCbEEIqQYWSEEIqQYWSEEIqUWtmYXTVdBRCcyabbRxPAMjMzERycrJX7Ed1X1+1Wo34+Hif3AeDwQCz2czfplvR7JGe5OznwjYurNlsLjMXu1CMRiMmTpzIT4/sSI0+1zW+ZN1HuGo6CqE5k02j0dh9X/J3hVSd1zcrK4sBYBaLxY3Jqs6ZfcjIyGBKpZJfluM4t+erquq+nxhj/D4JSafT8e+NytTkc10rCqXJZCpTJMRicY2X9TRnsmVlZdk9ZzKZGABmMpncmrEy1X19dTod4zjOKwqls/tQOrfQfwMbZ/ej9LLeUChtKiuUNf1c14o+SldNRyE0Z7JJJBIkJyfzP9sGOBZ63M3qvL56vR4KhcLd0arMmX0wm838uKlGoxFWq9UrDlcB5/8WwcHBkEql/CF4VFSUJ2K6RE0/17WiULpqOgqhOZutZHHZvn075HK54P17zu6D1WoVPHNpzuyD0WhEcHAw3zeWlJTEzx8vNGf/FrbRusLCwqDT6bzqn1dlavq5rjUnc8rjqukohFZZNqvVCr1eX2lnt5Ac7UNaWhqUSqVnw1RTefuQn58Ps9nM/5NSKpVo0qQJmBff5+Hob2EwGKDRaGA2mxEXFwcA0Gq1HkzmelX9XNeKFqWrpqMQWnWzqdVqZGRk+Nw+GAwGjBw50kPJqs6ZfeA4zm7g6ZIDVgvNmf0wm83IzMyEXC6HUqmEyWRCWlpamWmkvVVNP9e1olC6ajoKoVUnW2JiItRqNTiOg9VqFbxl7Ow+pKWlISkpCUlJSTCbzUhISBC8yDizD97SH1keZ/bDaDQiMjKS/5njOMTHxwv+fqqqmn6ua0WhrMp0FLb/jJUtKyRn9gN4cBJEIpHwRTItLU3w/XBmH2ytF9sXAMTFxUEikXg0c2nOvp9kMhlfUGzXUgq9D4Bz+yGRSJCZmWm3fF5enlfsh03pou3Sz3V1TsX7IpPJxFQqFdPpdEylUtldrqFQKOyuEatoWaFVdT9slwOV/PKmy5yq+rdgjDGLxcI0Gg0DwJRKJcvKyvJw4rKc2QeLxcKUSiXTarVMqVR6zeVBjDm3HxkZGUyj0TCtVsu0Wq1X7EdGRgZTqVQMAL8fNq78XNPoQYQQUolacehNCCE1QYWSEEIqQYWSEEIqQYWSEEIqQYWSEEIqQYWSEEIqQYWSEEIqQYWSEEIqQYWSEEIqQYWSEEIqUavHoyS1i21kbpPJhLi4OBiNRmRmZnrNhGXEe1GLktQaBoMBSqUSUVFRiI6OhkKhgF6v94rR64l3oxYlqTVsgwAbjUbExMQAAEwmk5CRiI+gFiWpNWyH19u3b+fne/GVgWeJsKhQklohKSkJarWaH8zVNpBrWlqawMmIL6DxKEmtYDAYYDabERwcDLFYzI987SsTlxFhUaEkhJBK0KE3IYRUggolIYRUggolIYRUggolIYRUggolIYRUggolIYRUggolIYRU4v8Be8c/xNC6T9cAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 350x262.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scienceplots # 导入'science'画图模块\n",
    "plt.style.use('science') # 采用'science'画图模块\n",
    "fig, ax = plt.subplots() # 建立画布\n",
    "x = np.linspace(0,1,100) # x轴点数\n",
    "y1 = -np.sqrt(30)*x*(x-1) # 近似解\n",
    "y2 = np.sqrt(2) *np.sin(np.pi* x) # 精确解\n",
    "ax.plot(x,y1,linewidth = '0.7',label=r'Approximate solution',color = 'k',linestyle='--') \n",
    "ax.plot(x,y2,linewidth = '0.7',label=r'Exact solution',color = 'k') \n",
    "ax.set_xlabel('$x$') # 设置横坐标名称\n",
    "ax.set_ylabel('$y(x)$') # 设置总坐标名称\n",
    "ax.spines['right'].set_visible(False) # 不显示右边框\n",
    "ax.spines['top'].set_visible(False) # 不显示上边框\n",
    "ax.legend() # 显示标签\n",
    "visible_ticks = { # 设定参数以不显示上和右刻度\n",
    "   \"top\": False,\n",
    "   \"right\": False\n",
    "}\n",
    "ax.tick_params(axis=\"both\", which=\"both\", **visible_ticks) # 去处上和右刻度\n",
    "fig.savefig('Ritz_fig1.png',dpi=600) # 保存图片\n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b17e30d6-6c73-4520-bafd-c65475c1d028",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -14.4913767461894$"
      ],
      "text/plain": [
       "-14.4913767461894"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N(sol_2[0][0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cb870bd2-86b8-4a00-a3b7-07c2939177d9",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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